Indefinite Definition and 299 Threads

An indefinite pronoun is a pronoun which does not have a specific familiar referent. Indefinite pronouns are in contrast to definite pronouns.
Indefinite pronouns can represent either count nouns or noncount nouns. They often have related forms across these categories: universal (such as everyone, everything), assertive existential (such as somebody, something), elective existential (such as anyone, anything), and negative (such as nobody, nothing).Many languages distinguish forms of indefinites used in affirmative contexts from those used in non-affirmative contexts. For instance, English "something" can only be used in affirmative contexts while "anything" is used otherwise.Indefinite pronouns are associated with indefinite determiners of a similar or identical form (such as every, any, all, some). A pronoun can be thought of as replacing a noun phrase, while a determiner introduces a noun phrase and precedes any adjectives that modify the noun. Thus all is an indefinite determiner in "all good boys deserve favour" but a pronoun in "all are happy".

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  1. J

    MHB Integral Evluation: $$\displaystyle \int\frac{5x^3+3x-1}{(x^3+3x+1)^3}dx$$

    Evaluation of $$\displaystyle \int\frac{5x^3+3x-1}{(x^3+3x+1)^3}dx$$$\bf{My\;Try::}$ Let $\displaystyle f(x) = \frac{ax+b}{(x^3+3x+1)^2}.$ Now Diff. both side w. r to $x\;,$ We Get$\displaystyle \Rightarrow f'(x) = \left\{\frac{(x^3+3x+1)^2\cdot a-2\cdot (x^3+3x+1)\cdot (3x^2+3)\cdot...
  2. R

    MHB Three indefinite integrals involving e^x

    Thank you :)
  3. P

    The Difference Between Two Indefinite Integrals

    I actually came across this question on social media. What is: $$\int sin (x) \, dx - \int sin (x) \, dx$$ And I think the answer depends on how we interpret: $$\int sin (x) \, dx$$ If we think of it as a single antiderivative, the answer would be zero. If we think of it as being...
  4. G

    Can You Crack This Challenging Indefinite Integral?

    Hello, everyone I've trying to solve this integral but it seems like the methods I know are not enogh to solve it. So I'd be glad if you could give me some trick to get into the answer. Here it is: Thanks in advance!
  5. P

    Arc Length: Definite and Indefinite Integration

    Several authors state the formula for finding the arc length of a curve defined by ##y = f(x)## from ##x=a## to ##x=b## as: $$\int ds = \int_a^b \sqrt{1+(\frac{dy}{dx})^2}dx$$ Isn't this notation technically wrong, since the RHS is a definite integral, and the LHS is an indefinite integral...
  6. H

    Limit Definition of Indefinite Integrals?

    Hello, I was just wondering, we have what could be called the indefinite derivative in the form of d/dx x^2=2x & evaluating at a particular x to get the definite derivative at that x. But with derivation, we can algebraically manipulate the limit definition of a derivative to actually evaluate...
  7. P

    What Is the Correct Evaluation of the Indefinite Integral of Zero?

    Argument A ##∫ 0 dx = 0x + C = C## Argument B ##∫ 0 dx = ∫ (0)(1) dx = 0 ∫ 1 dx = 0(x+C) = 0## Discuss.
  8. J

    MHB How Do You Solve the Integral of \( e^{x^4} (x + x^3 + 2x^5) e^{x^2} \, dx \)?

    \displaystyle \int e^{x^4}\left(x+x^3+2x^5\right)\cdot e^{x^2}dx =
  9. J

    MHB How to Calculate the Indefinite Integral of a Complex Function?

    Calculation of $\displaystyle \int \frac{\sqrt[4]{x^{10}+x^8+1}}{x^6}\cdot \left(3x^{10}+2x^{8}-2\right)dx$ $\bf{My\; Try::} $ Given $\displaystyle \int \frac{\sqrt[4]{x^{10}+x^8+1}}{x^6}\cdot \left(3x^{10}+2x^{8}-2\right)dx = \int\frac{\sqrt{x^6+x^4+x^{-4}}}{x^5}\cdot...
  10. P

    MHB Johnsy's question about finding an indefinite integral

    The big clue here is the square root in the denominator, because $\displaystyle \begin{align*} \frac{\mathrm{d}}{\mathrm{d}x} \left( \sqrt{x} \right) = \frac{1}{2\,\sqrt{x}} \end{align*}$. So this suggests that you probably need to find a square root function to substitute. Rewrite your...
  11. J

    MHB Evaluation of Indefinite Integral

    Calculation of \(\displaystyle \int\frac{\sqrt{\cos 2x}}{\sin x}dx\) **My Try \(\displaystyle :: I = \int\frac{\sqrt{\cos 2x}}{\sin x}dx = \int\frac{\cos 2x}{\sin x\cdot \sqrt{\cos 2x}}\cdot \frac{\sin x}{\sin x}dx = \int\frac{\sqrt{2\cos^2 x-1}}{\left(1-\cos^2 x\right)\cdot \sqrt{2\cos^2...
  12. J

    What is the indefinite integral of cosecant function?

    What is the indefinite integral of cosec(\theta)?
  13. J

    Indefinite Integrals of Scalar and Vector Fields: A Path Independence Dilemma?

    Is possible to compute indefinite integrals of functions wrt its variables, but is possible to compute indefinite integrals of scalar fields and vector fields wrt line, area, surface and volume?
  14. L

    MHB Help with Solving Indefinite Integral

    Hi, I tried to solve this integral \int\sqrt{1-\frac{1}{x^3}}dx but i can't solve it... can someone help me?
  15. J

    Find indefinite integral function, if definite integral value is know

    Is this possible.. Say, a∫b f(x)dx = G(x)|x=b - G(x)|x=a = S, where S, a and b are known. Can we find G(x) ?
  16. J

    MHB Trig. Indefinite Integral

    Evaluation of $\displaystyle \int\sqrt\frac{1+\tan x}{\csc^2 x+\sqrt{\sec x}}dx$ I have Tried The Given Integral Using $\displaystyle \tan x = \frac{2\tan \frac{x}{2}}{1-\tan^2 \frac{x}{2}}$ and $\displaystyle \cos x = \frac{1-\tan^2 \frac{x}{2}}{1-\tan^2 \frac{x}{2}}$ and $\displaystyle \sin x...
  17. J

    MHB Solving $\displaystyle \int \frac{\ln\left(x^2+2\right)}{(x+2)^2}dx$ by Parts

    $\displaystyle \int \frac{\ln\left(x^2+2\right)}{(x+2)^2}dx$ $\bf{My\; Try::}$ Given $\displaystyle \int \ln \left(x^2+2\right)\cdot \frac{1}{(x+2)^2}dx$ Using Integration by parts, we get $\displaystyle = -\ln\left(x^2+2\right)\cdot \frac{1}{(x+2)} + 2\int \frac{x}{\left(x^2+2\right)\cdot...
  18. L

    What is the Indefinite Integral of x*cos(3x)^2?

    Homework Statement Evaluate the indefinite integral of x*cos(3x)^2 Homework Equations Integration by parts: \int(udv)= uv - \int(vdu) The Attempt at a Solution Im having trouble finding the antiderivative of cos(3x)^2 (which I designated as dv when doing integration by parts). I...
  19. F

    Integration - Indefinite - By Parts and U-Sub

    Homework Statement Integrate the following indefinite integrals A:\int e^x (x^2+1) dx B:\int e^x cos(3x+2) dxHomework Equations \int u dv = uv - \int v du The Attempt at a Solution Part A: I have done the following but when I use an integration calculator online its not what I have (although...
  20. AntSC

    Indefinite integrals with different solutions?

    Indefinite integrals with different solutions? Homework Statement \int \csc ^{2}2x\cot 2x\: dx Solve without substitution using pattern recognition Homework Equations As above The Attempt at a Solution To try a function that, when differentiated, is of the same form as the...
  21. S

    MHB Evaluating the indefinite integral.

    How does \int \frac{2x + 2}{x^2 + 2x + 5} \, dx turn into \ln(x^2 + 2x + 5)? How are they getting rid of the numerator are they just dividing by the reciprocal of 2x + 2?
  22. KingCrimson

    Why do we write dx in indefinite integrals

    in understand why we write the dx in riemann integral , but in the indefinite integral why do we use that ? what is the relation between the area under a curve , and the antiderivative of that of that curve ??
  23. P

    MHB Indefinite Integral using Trig Identity i'm confused

    Okay so I'm working on this problem \int \frac{x^2}{\sqrt{4 - x^2}} \, dx I do a substitution and set x={\sqrt{4}}sinu I get to this step fine \int 4sin(u)^2 I know that u = arcsin(x/2) so I don't see why I can't just substitute in u into sin(u)? I tried this and I got \int 4 *...
  24. J

    Why is there a differential in an indefinite integral?

    I understand why a definite integral of the form ^{b}_{a}∫ƒ(x)dx has the differential dx in it. What I don't understand, and what my teacher hasn't explained is why an indefinite integral (i.e. an antiderivative) requires the differential. Why does ∫ƒ(x)dx require that dx to mean...
  25. MarkFL

    MHB Jamie's question at Yahoo Answers regarding an indefinite integral

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  26. W

    Indefinite trigonometric integral with an Nth Root

    Homework Statement Solve: \int sin(16x) \sqrt[a]{cos(16x)}\,dx Answer should be linear in the constant "a" The Attempt at a Solution \int sin(16x) \sqrt[a]{cos(16x)}\,dx Set: u=cos(16x), du=-16sin(16x) du ~~\Rightarrow~~ {-1/16}\int \sqrt[a]{u}\,du =...
  27. MarkFL

    MHB Mahnoor Jafer's question at Yahoo Answers regarding an indefinite integral

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  28. Y

    An indefinite integral with no constant of integration

    I this old thread it mentions that the indefinite integral of f'(x)/f(x) is log(|f(x)|)+C which means that there is some ambiguity about the sign of f(x). There does however, seem to be no ambiguity about the value of C as it always appears to be zero, but I have never seen this mentioned...
  29. MarkFL

    MHB Anh Nguyen's questions regarding indefinite integrals (integration by parts)

    Here are the questions: I have posted a link there to this thread so the OP can see my work.
  30. A

    Help finding an indefinite integral

    I am trying to find the following indefinite integral: Homework Statement ∫\sqrt{}x/(x-1)dx Homework Equations None The Attempt at a Solution I tried to use substitution but got nowhere. I set u=\sqrt{}x so du=1/(2\sqrt{}x)dx. However from here on on I got stuck. I also tried...
  31. MarkFL

    MHB Pillar of Autumn's question at Yahoo Answers regarding an indefinite integral

    Here is the question: I have posted a link there to this thread so the OP can see my work.
  32. MarkFL

    MHB What Is the Integral of sqrt(x-1)/x?

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  33. J

    MHB Integrating Trigonometric Functions with Multiple Substitutions

    [1] $\displaystyle \int\sqrt{\frac{\csc x-\cot x}{\csc x+\cot x}}\cdot \frac{\sec x}{\sqrt{1+2\sec x}}dx$ [2] $\displaystyle \int \frac{3\cot 3x - \cot x}{\tan x-3 \tan 3x}dx$ Thanks pranav I have edited it.
  34. J

    MHB Integrating $\frac{1}{(a+b\sin x)^2}dx$: Step-by-Step Guide

    $\displaystyle \int\frac{1}{(a+b\sin x)^2}dx$, where $a>b$ My Trial :: Using Integration by parts:: $\displaystyle \int\frac{1}{(a+b\sin x)^2}dx = \frac{1}{b}\int -\csc (x)\cdot \frac{-b\sin x}{(a+b\sin x)^2}dx$ $\displaystyle -\frac{1}{b}\cdot \csc (x)\cdot \frac{-1}{(a+b\sin x)}+\int...
  35. F

    MHB Indefinite integral with two parts

    I'm trying to integrate \int e^{4\ln{x}}x^2 dx I can't see using u-substition, x^2 isn't the derivative of e^{4\ln{x}} nor vice-versa. I tried integrating by parts and that didn't work. I used u=e^{4\ln{x}} and dv=x^2 dx I know I can't rewrite e^{4\ln{x}} as e^4e^\ln{x}
  36. J

    MHB How to Solve These Two Indefinite Integrals?

    $(a)\;\;:: \displaystyle \int\frac{1}{\left(x+\sqrt{x\cdot (x+1)}\right)^2}dx$ $(b)\;\;::\displaystyle \int\frac{1}{(x^4-1)^2}dx$ My Trial :: (a) $\displaystyle \int\frac{1}{(x+\sqrt{x\cdot (x+1)})^2}dx$ $\displaystyle \int\frac{1}{x\left(\sqrt{x}+\sqrt{x+1}\right)^2}dx =...
  37. paulmdrdo1

    MHB Solving Indefinite Integral: $\displaystyle\int\frac{dy}{1+e^y}$

    how would start solving this $\displaystyle\int\frac{dy}{1+e^y}$
  38. W

    Rewrite Indefinite Integral in Terms of Elliptic Coordinates

    Problem: Rewrite the indefinite integral ## \iint\limits_R\, (x+y) dx \ dy ## in terms of elliptic coordinates ##(u,v)##, where ## x=acosh(u)cos(v) ## and ## y=asinh(u)sin(v) ##. Attempt at a Solution: So would it be something like, ## \iint\limits_R\, (x+y) dx \ dy =...
  39. T

    Solve Indefinite Integral: ∫1/sqrt(x2-1)^5 dx

    Homework Statement Sorry for the poor use of Latex, I have tried to get it to work but it seems to never come out as I would like. Using a trigonometric or hyperbolic substitution, evaluate the following indfe nite integral, ∫\frac{1}{\sqrt{(x^2-1)^5}} dx Homework Equations I...
  40. paulmdrdo1

    MHB Solve Indefinite Integral: $\int\frac{\arctan x}{1+x^2}dx$

    how would i go about solving this $\displaystyle\int\frac{\arctan x}{1+x^2}dx$? i tried substitution but i didn't work.
  41. MarkFL

    MHB Solve Indefinite Integral of lnx/(1+x^2)^(3/2): Vuk's Q&A on Yahoo Answers

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  42. MarkFL

    MHB Ali's question at Yahoo Answers regarding an indefinite integral

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  43. MarkFL

    MHB JoHn eDwArd's question at Yahoo Answers regarding an indefinite integral

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  44. mathworker

    MHB How Do You Solve This Complex Indefinite Integral?

    This is the integral I am trying to evaluate. I would very much appreciate any help. \[\int \frac{2x^3-1}{x+x^4}dx\] MY APPROACH: \[\int \frac{2x^3-1}{x+x^4}dx\] \[\int \frac{1}{2}.(\frac{4x^3+1}{x^4+x}-\frac{3}{x^4+x})dx\] \[\frac{1}{2}\log{x+x^4}-\frac{1}{2}\int \frac{3}{x^4+x})dx\] now we...
  45. Z

    Tricky indefinite integral problem

    Homework Statement Ok the problem is: ∫-1/(4x-x^2) dx The answer in the back of the book is: (1/4)ln(abs((x-4)/x))) + C Homework Equations I think this would be used somehow: ∫ du/(a^2-u^2) = 1/2a ln(abs((a+u)/(a-u))) + C The Attempt at a Solution ∫-1/(4x-x^2) dx...
  46. MarkFL

    MHB Bob's question at Yahoo Answers regarding an indefinite integral

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  47. J

    Solving Indefinite Integrals: ∫1/(t*ln(t)) & ∫1/(√(t)*[1-2*√(t)])

    Homework Statement ∫1/(t*ln(t)) dt ∫1/(√(t)*[1-2*√(t)]) dt Homework Equations The Attempt at a Solution I used u-substitution for both. For the first equation, my u= ln t, and my final answer was ln|u| + C, or ln(ln(|t|) + C. For the second equation, my u= 1-2*√(t) and...
  48. Saitama

    How Do You Simplify the Expression (x-xcos^2x+cosxsinx)/sinx(xcosx-sinx)?

    Homework Statement \int \left(\frac{x}{x\cos x-\sin x} \right)^2 dxHomework Equations The Attempt at a Solution Factoring out ##\cos x## from the denominator, the integral transforms to \int \sec^2x \left(\frac{x}{x-\tan x}\right)^2dx Substituting ##\tan x=t##, ##\sec^2 xdx=dt## \int...
  49. Saitama

    Solving the Indefinite Integral of a Trigonometric Expression

    Homework Statement \int \sqrt{\frac{\csc x-\cot x}{\csc x+\cot x}} \frac{\sec x}{\sqrt{1+2\sec x}}dxHomework Equations The Attempt at a Solution The integral can be simplified to: \int \sqrt{\frac{1-\cos x}{1+\cos x}} \frac{1}{\sqrt{\cos x} \sqrt{\cos x+2}}dx Using ##\cos...
  50. I

    Find the indefinite integral by u-sub

    Homework Statement \int1/(1+\sqrt{2x})\,dx Homework Equations u=1+\sqrt{2x} \Rightarrow \sqrt{2x}=u-1 du=1/\sqrt{2x}dx \Rightarrow \sqrt{2x}du=dxThe Attempt at a Solution \int1/(1+\sqrt{2x})\,dx = \int\sqrt{2x}/(1+\sqrt{2x})\,du = \int(u-1)/u\,du = \int\,du-\int1/u\,du = u-ln|u|+C =...
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