Indefinite Definition and 299 Threads

Here is the question: Here is a link to the question: Find the indefinite integral? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Evaluate the indefinite integral as an infinite series ∫ sin(x2) dx Homework Equations The Macluarin series of sin x = ∞ Ʃ (-1)nx2n+1/(2n+1)! n=0 The Macluarin series for sin(x2) = ∞ Ʃ (-1)x4n+2/(2n+1)! n=0 The Attempt...

Here is the question: Here is a link to the question: Calc 2 integral question? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hello everyone.. Homework Statement ∫√((1+(e^-x))^2)dx 2. The attempt at a solution I first tried to do a u sub and then attempt a trig sub however I can't do anything with the e^-x left in the u sub. Does anyone have another way I can integrate this thing?? Thank you for any suggestions/help!

Here is the question: Here is a link to the question: Integration question!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Ʃ(x-->infinity, x>0) 11/(n(n+2)) Homework Equations The Attempt at a Solution I am not quite sure what to do, i think that i am supposed to put it into partial fractions. i changed it to the form 11/(n^2+2n) --> 11/((n+1)(n+1)-1)) --> 11/((n+1)^2-1)...

Homework Statement ∫(x3 - 3x2 + x + 1)/√x dx The Attempt at a Solution ∫x3-1/2 - 3∫x2-1/2 + ∫x1-1/2 + ∫x1-1/2 ∫x5/2 - 3∫x3/2 + ∫x1/2 + ∫1/2 (x7/2)7/2 - (3x5/2)5/2 + (x3/2)3/2 + (x3/2)3/2 + C (2x7/2)/7 - (6x5/2)/5 + 2x3/2)/3 + (2x3/2)/3 + C Thank you so much!

Homework Statement Integrate (3x^2-10)/(x^2-4x+4) dx using partial fractions. Homework Equations None The Attempt at a Solution I tried using A/(x-2) + B/(x-2)^2 but I didnt get a coeffecient of an x^2. I've also tried using (Ax+B)/(x-2) + C/(x-2)^2 Though I...

It's been a year since I took Calc I, and I'm taking Calc II online this semester. This is technically a review problem from Calc I, and I managed the other seven, but I can't figure out how to solve this problem. 1.a Homework Statement ∫(a*sin(14x))/(\sqrt{1-196x^2} dx, evaluated at x=0...

Homework Statement ∫▒〖(4x^2+2√x+1)/(2x√x) dx〗 Homework Equations The Attempt at a Solution ∫▒〖(4x^2+2√x+1)/(2x√x) dx〗 ∫▒((4x^2)/(2x^(3/2) )+(2√x)/(2x^(3/2) )+1/(2x^(3/2) ))dx 2∫▒x^(1/2) dx+∫▒〖x^(-1) dx〗+1/2 ∫▒x^(-3/2) dx 2×2/3 x^(3/2)+ln⁡x+1/2×(-2) x^(-1/2)+C 4/3...

Homework Statement I do not know how to solve the following indefinite integral. I personally think it is very difficult and would appreciate it had someone can explain it step by step? Homework Equations / The Attempt at a Solution This integral must been solved by mix of...

I understand that the indefinite integral is like infinite definite integrals, but how come when we calculate the definite integral we simply substitute the two values into the indefinite integral and subtract? Why do we subtract? Why not add? Also, there aren't the same thing, right? What's...

Hi, Rather simple question here, just want to confirm: When we are dealing with indefinite double integrals, it's true to say ∫∫ f(x,y) dx dy = ∫∫ f(x,y) dy dx i.e, order of integration doesn't matter right?

Homework Statement F(x)= (3^x)(e^x)dx Homework Equations F(u)=U^n=(U^(n+1))/n+1 The Attempt at a Solution I said it equaled: ((3^(x+1))/(x+1))(e^x)

$\displaystyle \int\sqrt{\frac{x^2+1}{x^2-1}}dx$

Hi, I've been wondering this since I started learning integration. I get that ∫ is basically an elongated S for "sum", because that is what it is basically doing. But then Ʃ does the same thing as well. If I'm understanding the difference, it is that Ʃ increments by finite measures, whereas ∫...

$(1)\displaystyle \;\; \int\frac{1}{1+x^6}dx$ $(2)\displaystyle \;\; \int\frac{1}{1+x^8}dx$

$\displaystyle \int\frac{1}{\sqrt[4]{1-x^4}}dx$

Homework Statement Evaluate the integral: ∫ {√[(a^2)-(x^2)] / (b-x)} dx Homework Equations ∫ u dv = uv - ∫v du The Attempt at a Solution I've tried using integration by parts but it makes the integral even more complex. I also tried using the table of integrals to find a solution to no...

Homework Statement I hope this is in the right forum, because this is a question on theory and not related to a specific problem. I was reading onlne about the Fundamental Theorem of Calculus. On one site the author wrote: F(x) = \int_{0}^{x} f(t) dt Later, he wrote: \int_{a}^{b}...

Homework Statement Compute the following: \int \frac{cosh(x)}{cosh^2(x) - 1}\,dx Homework Equations \int cosh(x)\,dx = sinh(x) + C The Attempt at a Solution I had no clue where to start, so I went to WolfRamAlpha, and it used substitution but it made u = tanh(\frac{x}{2})...

Homework Statement Find the function f(x) such that f''(x) = \frac{1}{x^2}, f(1) = 0 and f(e) = 0 Homework Equations \int f''(x)\,dx = f'(x) + c \int f'(x)\,dx = f(x) + cx + C The Attempt at a Solution f''(x)= \frac{1}{x^2} f'(x)= \int \frac{1}{x^2}\,dx = \frac{-1}{x} + c f(x) = -\int...

Homework Statement The value of \int_0^{1} (\prod_{r=1}^{n} (x+r))(\sum_{k=1}^{n} \frac{1}{x+k}) dx equals: a)n b)n! c)(n+1)! d)n.n! (Can someone tell me how to make bigger parentheses using latex?) Homework Equations The Attempt at a Solution I know that the question becomes...

Homework Statement <Indefinite integral sign here>[r^2 -2r] / [r^3 - 3r^2 + 1]dr or the second example in the "Substitution" section here: http://people.clarkson.edu/~sfulton/ma132/parfrac.pdf Homework Equations nada. The Attempt at a Solution Nothing to really attempt, I just...

Indefinite Integration of function's like log(cos(x))? Can anyone please help me to calculate Indefinite Integration of function's like log(cos(x))?.

EDIT: Problem found. This thread can now be ignored.Homework Statement Find the indefinite integral. Homework Equations ((y^2-1)/y)^2 dy The Attempt at a Solution I've attempted a few things. I first attempted to split the statement inside the outer parentheses into two fractions; (y^2/y...

Hello! Permissible is probably the wrong word, but here's what I am having difficulty with: With substitutions in integration to make the integral easier to solve, there doesn't seem to be a restriction on the substitution one can use with indefinite integration. If one function, or part...

Hello, I have recently encountered an integral that I have been able to evaluate in a sick, unholy way, and for making a proof much more elegant I would like a simple way to evaluate the integral from 0 to infinity of ln(x)/(e^x+1) . thank you!

Homework Statement Well I have these three different integrals: \int{\frac{1}{\sqrt{4x^2-1}}dx} \int{\frac{1}{4-x^2}dx} \int{\frac{1}{x^2+4x+8}dx}Homework Equations Yeah well not exactly sure how to approach this... Do you use integration by substitution, where you come up with some...

Homework Statement Calculate the following integral: \int{\frac{\sqrt{x+1}}{x+5}dx} \ , x ≥ 1 By using the following substitution: t=\sqrt{x+1} Homework Equations Well using the integration by substitution formula. The Attempt at a Solution So I have t=\sqrt{x+1}...

Presently, I am reading about computing definite integrals; and in one of the examples the authors provides, there is a statement made: "Recall that the point behind indefinite integration...is to determine what function we differentiated to get the integrand." I was wondering if someone...

Homework Statement 1 / (3√x2 ) Homework Equations The Attempt at a Solution the overall power of x in denom becomes ( 1/2 * 2 * 1/3 = 1/3) taking in num , it becomes (-1/3 + 1 = 2/3) so answer should be x2/3 / (2/3) which is wrong , please help

Homework Statement Given:lim_{n\rightarrow ∞} \int^{a^n}_{1} \frac{t^{1/n}}{(1+t)t} dt=\int^{∞}_{1} \frac{1}{(1+t)t} dt a - Natural number. I need to prove that I can bring limit under the integral sign. Homework Equations The Attempt at a Solution I've got this so far: | \int^{a^n}_{1}...

Homework Statement ∫8x3e-cos(x4+4)sin(x4+4)dx Homework Equations Let u = cos(x4+4) The Attempt at a Solution I know the answer does not have the sin in it and only the e remains, because when the integral is found e stays unchanged. I could find somewhere online to calculate it...

∫(tanxsec^{2}x)dx <---Original function to integrate. I do: ∫(tanxsec^{2}x)dx ---> ∫(tanx\frac{1}{cos^{2}x})dx ---> ∫((\frac{sinx}{cosx})(\frac{1}{cos^{2}x}))dx ---> ∫(\frac{sinx}{cos^{3}x})dx ---> substitution: [t=cosx , dt=-sinxdx -> [itex]\frac{dt}{-sinx}[/itex]=dx] --->...

*SOLVED* Indefinite integrals. Arriving at different results. Mistake found. Thanks!, everything looks correct now.

$\displaystyle \int \frac{e^x}{1+x}dx$

Homework Statement ∫ 1/x arctan (lnx) dx Homework Equations The Attempt at a Solution 1.U substitution. SO u = ln x, du= 1/x dx ∫ arctan u du 2.by parts: u = arctan u du = 1/ 1+u^2 v = 1 dv = du 3. uv - ∫vdu = artan u - ∫ 1/ 1+u^2 =...

$\displaystyle \int \frac{1}{\sqrt{\sin 2x}}dx$

Homework Statement find the indefinite integral of ∫x√(1-x^2) dx Homework Equations The Attempt at a Solution ∫x√(1-x^2) dx let x = sinθ dx = cosθ dθ now sin^2θ + cos^2θ = 1 => cosθ = √1-sin^2θ ( for the form √(1-x^2)) ∫x√(1-x^2) dx => ∫sinθ (√1-sin^2θ) cosθ dθ =>...

Homework Statement a) S 13(4^x + 3^x)dx b) S (cosx + sec^2x)dx c) S (3-(1/x))dx d) S e^(7x)dx Homework Equations The S is supposed to be the integration sign The Attempt at a Solution Are these correct or at least close? a) = 13((4^x)/(ln(4) + (3^x)/(ln(3))) + C b) =...

Interpretation of "dx" as the differential of x for Indefinite Integrals This question is concept-as-opposed-to-calculation based. I understand that when one sees the integral sign, followed by f(x)dx, that we can think of this as the indefinite integral, or antiderivative of f(x), with...

Homework Statement Find the indefinite integral (preferably using u-substitution): ∫(ex-e-x)2 dx Homework Equations N/A The Attempt at a Solution To be honest, I'm slightly confused as to which path I'm supposed to take with this, especially since I'm not sure what I should be...

Say we are solving an indefinite integral ∫x√(2x+1) dx. According to the textbook, the solution goes like this. Let u = 2x+1. Then x = (u-1)/2. Since √(2x+1) dx = (1/2)√u du, x√(2x+1) dx = [(u-1)/2] * (1/2)√u du. ∫x√(2x+1) dx = ∫[(u-1)/2] * (1/2)√u du. <= What justifies this?? The...

Homework Statement *indeterminate* oops the limit of x^x as x goes to zero from the right Homework Equations Going to be using L'hopital, and related algebraic manipulations to convert to indefinite form 0/0, infinity/infinity The Attempt at a Solution My understanding is that this limit...

Homework Statement \int(x^(1/3)/(x^(1/3)+1))dx Homework Equations I know I have to use u substitution u=x^(1/3) du=1/(3x^(2/3))dx The Attempt at a Solution I know that the denominator of the equation will be u+1, but I don't understand how to find the numerator because I thought...

Homework Statement hey could you help me to calculate the indefinite integral of y=√(x+1)/√(x+2) Homework Equations The Attempt at a Solution tried to set x+1=u and integrate it by substitution but didnt work

A calculus book I am looking at ("Early Transcendentals") does not seem to mention it, but it seems like it is possible, with the constants of integration being functions that have no component in variable being used for the integration. Any insight? Articles?

I'm having a problem with the following integral: x^3/sqrt[1 + x^2] dx Can this be done with substitution or integration by parts? Throw me some hints at this one please! Sorry I forgot to include my attempt. I tried solving this by substitution, letting u=1-x^2. Then letting (-1/2)du =...

Hi guys, I don't even know where to begin with this question. Find the following indefinite integral: \int x.arsinh (x^2) dx Thanks very much for any help, its much appreciated.