Indefinite integral Definition and 207 Threads

∫(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] --->...

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

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 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 \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

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.

Hello, I need help with a very hard integral, I was trying several steps and I tried in the software "derive" but the answer didn't like to me. It is ψ(x,t)= [b^2-(x-vt)^2]^(-2) . I must integrate it with respect to x . Thanks in advance for any help! PD: I tried x-vt = u like the...

Homework Statement A time-dependent torque given by a + bsin(ct) is applied to an object that's initially stationary but is free to rotate. Here a, b, and c are constants. Find an expression for the object's angular momentum as a function of time, assuming the torque is first applied at t =...

Homework Statement \int (\frac{x}{\sqrt{x+8}}) dx The Attempt at a Solution I got to be honest, I don't even really know where to start with this problem. So bear with me as I take a wild stab in the dark. This section was substitution problems, ... \frac{x}{\sqrt{x+8}} = \sqrt{...

Homework Statement Consider the integral, \int _3 ^7 (\frac{3}{x} + 2) dx a) Find the Riemann Sum for this integral using right endpoints and n=4. b) Find the Riemann Sum for this integral using left endpoints and n=4. Homework Equations The sum, \sum^{n = 4} (\frac{3}{x} + 2) The graph...

Homework Statement Evaluate the integral \int \frac{(a-x)^{r/s-1}}{(b-x)^{r/2}}dx Homework Equations given: s>r The Attempt at a Solution I tried using a substitution: let u=b-x so du=-dx this gives: -\int \frac{(a-b+u)^{r/s-1}}{u^{r/2}}du I don't know what i should...

Homework Statement The problem is divided into two sections: a) does the improper integral: 2ln(x)/x^7 (from 1 to infinity) Converge or diverge? If it converges, to what value? b) Determine whether the series: sigma n=1 to infinity (2ln(n)/n^7) converges or diverges. Homework...

Homework Statement I need help finding the anti-derivatives (indefinite integrals) of the 2 functions below: 1) e^(sqrt(x)) 2) Sqrt(2x - x^2) Homework Equations The Attempt at a Solution I tried forever at these 2 but I can't figure out a way for either of them. Any...

Homework Statement \int \frac{\sqrt{x^4-1}}{x^3}dx Homework Equations The Attempt at a Solution tried substituting x^4 = \sec^2 \theta to get rid of square root but it was of no use because, I got another complex integral \int \frac{\sin^2\theta}{\cos^{\frac{3}{4}}...

Anyone how to integrate this? Integration by parts doesn't get me anywhere, and there isn't a maclaurin series for ln(x). Thanks! (This isn't a homework question, I just was randomly doing integrals)

Homework Statement S=integral symbol S(5x+7)^28 Homework Equations Substitution The Attempt at a Solution let u = 5x+7 du = 5 S u^28 du = (u^29)/29 du = [5(5x+7)^29]/29 is this correct? I'm not sure...

Homework Statement \int{\sqrt{1+e^x}dx} Homework Equations \int{uv'}=uv-\int{u'v} The Attempt at a Solution I rewrote the integrand as \sqrt{1+(e^{x/2})^2} and used the trigonometric substituition e^{x/2}=tan(\theta), which simplified the radical to...

Hey, all. Anyway, browsing the Internet a bit I found this integral: \int \sqrt{1 + \frac{\ln x}{x}}dx as a proposed problem in a compilation of maths problems, as an integral from the MATYC journal. I gave it to Mathematica and WolframAlpha and they weren't able to solve it...

Given an indefinite integral, \int f(x) dx = F(x) + C, I am having some problems in understanding what this indefinite integral "is". The RHS is clearly a function, but what is the LHS? Judging by the equals sign, it should also be a function, but seemingly it isn't because there's no...

Homework Statement Evaluate the indefinite integral. Homework Equations I tried to use substitution. The Attempt at a Solution I'm not so good with using the LaTex codes...so I attached a file I made in Word. Thanks in advance!

Homework Statement indefinite integral 5\picos\pit Homework Equations The Attempt at a Solution 5\pi int cos\pit Substitution Method 5\pi x sin (1/\pit

Homework Statement (e^-x)/(1+e^-x)dx Homework Equations Integral of e^x function The Attempt at a Solution I am completely lost with the problem, the fact that it is e^-x and not e^x has me stupped as well as the division.

Homework Statement integral 1/(x(sqrt(x^2 - 4))) Homework Equations I don't know if there are any "equations" for integrals... The Attempt at a Solution Int(1/(x(Sqrt(4(x^2 /4)-1) Int(1/(2x(Sqrt((x^2 /4)-1) 1/2 int(1/(x(Sqrt((x /2)^2)-1) U-sub u=x/2 du=1/2 dx 2du= dx...

This question is bugging me if an indefinite integral is of the form F(x) + C stating that F(x) is an antiderivative of f(x) and since the derivative of a constant is 0 the collection of all of the anti derivatives are of the F(x) + C accounting for the fact any constant can be tagged to the...

I arrived at this problem while trying to find the length of a 3D http://en.wikipedia.org/wiki/Cubic_interpolation" . Basically, I'm having to figure out how to integrate ((At4+Bt3+Ct2+Dt+E)1/2)dt A,B,C,D, and E are constants which have to be plugged in after integration, I'm sorry to say...

Homework Statement How do I evaluate this? A hint will do.

Hello, I'm kind of stuck in this problem. I have to express the integral as a power series. the integral of (e^x -1)/x I thought about evaluating it as f(x)=(e^x -1)/x and treating it as a Taylor series is that correct? Could I have any other hints? I would really appreciate it...

Homework Statement I started the problem, got stuck. Homework Equations The Attempt at a Solution

Homework Statement Hi, can you please check the two problems? (I have never done such before) Homework Equations The Attempt at a Solution

Homework Statement Hi! Can anyone check if I got the right answer? The Attempt at a Solution

Homework Statement ∫cos(x)/sin^2(x)*dx Homework Equations The Attempt at a Solution Based off my earlier question, where is my error please. u=sinx du=cosx*dx ∫u^-1*du sin(x)^-1 1/sin(x) + C -or-csc(x) + C Thanks

Homework Statement ∫cos(x)sin^6(x)*dx Homework Equations The Attempt at a Solution u=sin(x) then du should be -cos(x) according to the integral tables? -∫u^6*du = -u^7/7 -sin^7(x)/7+c yet my book and calculator tell me the answer is positive. How?

1/(4+3x^2) ? I'm trying to use this integration formula to solve for this du ---------- a^2+u^2 I know my a would be 2, but what would my u be? I tried u = 3x and du=3dx and du/3=dx but (3x)^2 would be 9x^2

Homework Statement The problem reads(from the 4th edition of Stewart Calculus "Concepts and Contexts" pg. 394 #17): Evaluate the integral. the indefinite integral of dx/x^2*sqrt(4-x^2) so this would read out as "the indefinite integral of dx over x squared times the square root of 4 minus...

\int\frac{4}{-e^{4x-7}} =ln-e^{4x-7}} =-4x+7+C The answer says it is: =\-e^{-4x+7}+C

S x^2(e^((x^3)+1)) I know I have to use integration by parts, and I'm guessing I should find the derivative of e^((x^3)+1), but I really have no idea where to start...

Homework Statement how to solve the integral of x^3 - 3x^2 + 4x -9 / x^2 + 3 dx Homework Equations using long division The Attempt at a Solution x^2 + 3 divided into x^3 - 3x^2 + 4x -9 I am not sure

Homework Statement integral of 1/x^2/3(1+x^1/3) Homework Equations integral of 1/x dx = ln|x| + c The Attempt at a Solution let u= x ^2/3(1+x^1/3)

Homework Statement Integrate: ((e^arccos(x))(dx))/(sqrt(1-x^2)) Image of the question is attached. Homework Equations The Attempt at a Solution I think i took the right first step for substitution: u=arccos(x); cos(u)=x; (du)(-sin(u))=dx Substituting u into the...

Homework Statement I need to evaluate the following integral: \int_{-\infty}^{\infty}x^mx^ne^{-x^2}dx I need the result to construct the first 5 Hermite polynomials. Homework Equations The Attempt at a Solution First I tried arbitrary values for "m" and "n". I was not able to...

Homework Statement \int_1^\infty \! \frac{(sin(x)+5)}{x^3} \, dx "Find two simpler integrals, one larger and one smaller." Homework Equations The Attempt at a Solution How could I make this a simpler (ie, solvable) integral? It's been straight forward with other integrals like...

Homework Statement \int \frac{ \tan x \sec^2 x }{ \tan^2 x + 6 \tan x + 8 } dx Homework Equations The Attempt at a Solution \int \frac{ \tan x \sec^2 x }{ \tan^2 x + 6 \tan x + 8 } dx Okay I let... u=tanx du=sec^2x Then I got \int \frac{ u }{ (u+4)(u+2) } du Then...

Homework Statement I hope someone can help me with this integral. It is really an improper integral, but I cannot figure out how to do the indefinite integral on it: integral[e1/x/x3]. Any help would be appreciated, thanks. Homework Equations ? The Attempt at a Solution I...

1. Homework Statement [/b] \int e^{3x}\sqrt{1+e^{2x}dx Homework Equations Substitution Parts of Integration The Attempt at a Solution Started off using U substitution setting ex = to u. Then tried to use parts of integration. Now I am stuck.