Indefinite integral Definition and 205 Threads

Homework Statement Find the indefinite integral of 16x^2+36+1/(16x^2+36) with respect to x Homework Equations Anything possible to take an anti-derivative The Attempt at a Solution I have absolutely no idea on how to deal with this problem. I can take an anti-derivative of the...

Hi, Looking to integrate the indefinite integral: \int tan~x\cdot ln~x\cdot cos~x Since tan x = sin x/ cos x, this integral be written as \int sin~x\cdot ln~x In that case i thought the answer was cot x. But that is wrong. Do you need to use integration by parts on this one?

Homework Statement \int{ x^3 \sqrt{(36-x^2)}dx} Homework Equations The Attempt at a Solution I tried using trig substitution but got 7776\int{cos^3(\theta)-cos^5(\theta)d\theta} which seems completely wrong 6cos(\theta)=x 6sin(\theta)d\theta=dx...

Using U-substitution find the indefinite integral of: [sin(2x)/cos^4(2x)] dx So I do know that it will have to come out to it being ln... here's what i did so far ok so i made u= cos^4(2x) du= -8cos^3(2x)*sin(2x)dx...(just took the derivative of u and simplified it) so made sin(2x)dx=...

In a book while doing an indefinite integral the author first wrote (sec2 x)1/2 = |sec x| , fine , then the author says the following : "since we are doing an indefinite integral we can drop the absolute value bars" , now what is the justification for this ?

Homework Statement Evaluate the indefinite integral. \int \left({\sqrt[5]{x^5}}-\frac{6}{5 x}+\frac{1}{4 x^{7}} \right) dx The Attempt at a Solution O.k. the only anti-derivative I am having trouble getting is the first one {\sqrt[5]{x^5}}. I am not sure what formula I would use...

Homework Statement Hi, Our professor has only taught us these methods for Integration...thus far: Direct Integration Substituion Method So theoretically we should be able to solve this problem without using Integration by parts or partial fractions...: Integrate...

Homework Statement Solve the indefinite integral Homework Equations \int\frac{dy}{y(1-y)} How do I best approach this problem? I have been stuck for hours!

Homework Statement Hello, first of all I would like to apologize for the fact that this question is extremely trivial compared to the other questions being asked. I have a improper integral problem, and the entire problem itself is not relevant, because I understand everything in it except...

Homework Statement ∫(exp(6x))/(exp(12x)+25)dx Homework Equations answer: -arctan[5/exp(6*x)]/30 The Attempt at a Solution honestly, don't know where to start. i was looking at another forum and tried to set u=exp(x) du=exp(x) and dx=du/u. plugging that in i got u^6/(u^12+25)*du/u. not sure...

Homework Statement My daughter at college asked me to help her with these but it's been years since I've done them. I said I would try and then look over what she comes up with so any help would be great not so I can give her the answers but so I can tell her whether or not she on the right...

Homework Statement Find the average distance to the x-axis for points in the region bounded by the x-axis and the graph of y = x - x^2. Homework Equations The Attempt at a Solution Can someone guide me how to solve this?

Homework Statement Indefinite integral: e^(4x+(e^4x)) Homework Equations I'm thinking integration by parts, involving UV minus integral of Vdu The Attempt at a Solution So I saw that this can be split into two: e^(4x) times e^(e^4x)). The latter is a bit complicated. I...

Homework Statement If {\vec{V}(t) is a vector function of t , find the indefinite integral: \int (\vec{V}\times \frac{d^2\vec{V}}{dt^2}) \,dt Homework Equations The Attempt at a Solution I have solved it by decomposing and integrating each terms of vector \vec{V}\times \frac{d^2t}{dt^2}...

Homework Statement I wasn't really sure where to post this, as I don't need help understanding the integration. I need help with the trigonometry! That being said, here is the problem. Find the general indefinite integral of \int\frac{\sin{x}}{1-sin^2{x}}dx Homework Equations...

Find \displaystyle\int\dfrac{\sec ^2\sqrt{x}}{\sqrt{x}} dx We're supposed to use u du substitution but I can't seem to get this one. EDIT: Sorry I didn't read rules. I tried u=\sec^2\sqrt{x} and all variants. Usually it was in the form of [sec or cos][^2 or none][sqrt x]

A long time since i posted at physics forums. Anyways, try helping me solve the following integral \int\frac{1}{x^{2n} + 1}dx I tried many ways but all futile. The best way with which i could come up was factorising the denominator by de moivre's theorem. By finding the 2nth roots of...

Homework Statement 1. The calculation of the probability of excitation of an atom originally in the ground state to an excited state, involves the contour integral INTEGRAL(-INF TO +INF) [S exp(iwt)/(t2 + s2)2dt Evaluate the above integral. Homework Equations The Attempt at a...

Homework Statement Evaluate the following indefinite integral: (2t6-3)/t3 dt The Attempt at a Solution I know I need to substitute. Tried u= t3 and found du= 3t2dt. Tried to find where du would substitute in, but found...

Hey everybody, One question that I've had for a week or so now is how the following integral can equal a Dirac delta function: \frac{1}{2\pi} \int_{-\infty}^{\infty}{dt} \:e^{i(\omega - \omega^{'})t}\: = \: \delta(\omega - \omega^{'}) A text that I was reading discusses Fourier transforms...

Hi, I was wondering if a function is absolutely convergent over a certain interval, say, (0,\infty) will its indefinite integral also be absolutely convergent over the same interval? Also, assume that f(x) is convergent for (0,\infty). Would g(x) = \int{\int_{0}^{\infty}f(x)dx}dy &=&...

Evaluate this indefinite integreal S = integral S 1/(9+x^2)^2 This has been driving me and my friend nuts. We tried partial fractions only to realize that it brings us back to the same thing because its not a polynomial over a polynomial, we tried by parts and it did not help and we...

Homework Statement Find the constant, c, that satisfies the following equation: Homework Equations The integral is from -infinity to infinity 1 = c \int e ^ -|x|/2 *dx The Attempt at a Solution c = 1/4 I have the solution given to me, but I do not understand how to get the...

Homework Statement evaluate the integral ∫x^2 sinpi x dx Homework Equations ∫u dv= uv - ∫v du integration by parts formula The Attempt at a Solution u=x^2 dv= sin pi x dx du = 2x v = -cos pi x dx ? the pi is giving me trouble

of sin pi x dx i thought it would be - cos pi x dx but i think it might be (1/pi) -cos pi x dx

The integral of [sin^3*(13x)*cos^8*(13x)]dx I think u=sin^3 so du/dx=cos^3 du=cos^3dx but then I am really not sure if that is correct, the trig functions confuse me a bit. Please help me, thank you!

Evaluate the indefinite integral: [(e^(4x))/(e^(8x))+9]dx -I think that u=e^(2x) so then du=e^(2x)dx then the answer would end up being [(e^(4x)+9)/(-1)]^(-1) but it was incorrect; I think that my u might be wrong and that's where the problem is, but I am not sure. Please help, thank...

Homework Statement The integral of 5*(sin(6x)/sin(3x))dx The Attempt at a Solution I'm not quite sure what to do with this one. I moved 5 to the left of the integral, but then I'm lost. Apparently I'm rusty on these trig identities. Could anyone help me get started? Thank you.

Homework Statement What is the connection between the Indefinite integral and the Fundalmental theorem of calculus (1st part)? The Attempt at a Solution They are the same to me but the FT is more formal.

How can I evaluate \int\frac{dx}{\sqrt{1-2x-x^2}} using inverse trig functions? Thanks.

How to evaluate \int{\frac{\arccos{x}}{x^2}\,dx}?

Hi, I need help evaluating the following integral by integration by parts: \int(a^2-x^2)^n\,dx. Specifically I am supposed to prove the following formula: \int(a^2-x^2)^n\,dx=\frac{x(a^2-x^2)^n}{2n+1}+\frac{2a^2n}{2n+1}\int(a^2-x^2)^{n-1}\,dx+C Any hints would be appreciated. Also, does...

how to evaluate the indefinite integral \int \frac{1}{\sqrt{x^2-1}} dx

how to evaluate the indefinite integral ∫(x^2-1)^(-1/2) dx and ∫x^(-1)*(1-x^2)^(-1/2) dx

Don't understand why "an indefinite integral is valid only on a interval" Hi I'm using Stewart's Calculus, in the section of indefinite integral, they say: "Recall from Theorem 4.10.1 that the most general antiderivative on a given interval is obtained by adding a constant to a particular...

1. \int(x^{2} + 5)^{3}dx This is what the book gives as the answer 1/7x^{7} + 3x^{5} + 25x^{3} + 125x + C I got something way different. Where are they getting the 3x^5 and 25x^3 from? Thanks. -v.b.

Homework Statement How is this function continuous from 0 to infinity F(x) = \int\frac{1}{t}dt from x to 2x Homework Equations I am fairly sure that this equation uses the properties of natural logs to solve. Also an infinite function has a derivative that is equal to 0. The...

Helo everyone, can somebody post the best algorithm/strategy to solve indefinite integral questions which are usually asked to undergraduates. The most general set of steps that can be applied to every question one encounters in the classroom. Algo that though may be proved to be inconvenient...

Hi, here is the question integrate x^3/(x^5-1)

Homework Statement ok I am given this problem indef. int (1+tan^2*5x)dx i need to use the u subsitution method to find the answer but i cannot seem to find what to subsitute the worksheet says the answer is " one-fifth*tan5x+C Homework Equations The Attempt at a Solution

Problem: [int]cosx(sinx)dx Given: x=pi; f(pi)=13.4 I am utterly confused on how to solve this integral. I am 99% positive (which is nothing in the math world) that I need to apply the product rule to all of this in order to find the antiderivative. However, no matter how I think of going about...

There is a simple formula for calculating \frac{df(x)}{dx} u^n where u is a function of x and n is a positive rational number: \frac{df(x)}{dx} u^n = nu^{n-1} \ast \frac{du}{dx} . Is there a similar formula for calculating \int u^n dx where u is a function of x and n is a positive rational...

evaluate the indefinite integral cos^4(x)sin(x)dx I tried using the half angle formula but this gives me a much more difficult integral, so i resorted to just regular substitution but am not sure if I can do this. u = cos(x) du = -sin(x)dx indefinite integral -u^4du then -1/5(u)^5...

I'm supposed to integrate the following expression, and supposedly there is a very simple way to do so. Maple comes up with something rediculous, so I'd appreciate any input. Sorry about the short hand, don't know how to make everything pretty on here: Integral[(e^ax)cos^2(2bx)dx] where a and...

evaluate the indefinite integral ((e^x)/((e^x)+1))dx I let u = ((e^x)+1) then du = (e^x)dx which occurs in the original equation so.. indefinite ingegral ((u^-1)du) taking the antiderivative I get 1 + C is this right? thanks!

Hi everyone. I'm having some trouble evaluating the following integral \int{sin^4xdx} First let me start off by showing what I did. = \int{(sin^2x)(sin^2x)dx} =\int{[\frac{1}{2}-\frac{1}{2}cos(2x)] \ [\frac{1}{2}-\frac{1}{2}cos(2x)]dx...

I need to integrate this indefinite integral: 1/(x-6)^2 dx Here is my work... Let u= x-6 du/dx=1 so: integral 1/u^2 du = 3/u^3 + c (constant) =3/(x-6)^3 + c Have I gone wrong? And if so where? Thanks

I have: int (1/(sqrt -x^2 -2x))dx so I rewrite (-x^2-2x) --> 1-(x+1)^2 and swap those two. then I say t=x+1, and substitute that in. So now I have: int (1/(sqrt 1-t^2)) dt Here I get stuck, can anyone please help?

Evaluating indefinite integral -- toughie! I have the velocity function v(x) = [(k*x^2)/(2*m)] + v0 I need to integrate this to get position as a function of time. So v = dx/dt. Separating variables, I get t = Integral [2m/(2mv0 + kx^2)] Here's where I'm stuck...If i pull out the 2m, then I...

How do I find the indefinite integral of 1/[(e^x)+(e^-x)] ? Do I have to multiply by [(e^x)-(e^-x)]/[(e^x)-(e^-x)] to eliminate the denominator? !