Linked Questions

Im looking for Tips and Tricks for integration. I know all the basic techniques (substitution, completing the square, parts etc.) I'm mainly interested in dealing with logs in the denominator and ...

While going through some of my notes, I came across a formula for evaluating an integral of the form: $$\int_0^\infty {\frac{dx}{x^n+1}} = \frac{\pi}{n\sin(\frac{\pi}{n})}$$ I was wondering if any ...

So far, I know and can use a reasonable number of 'tricks' or techniques when I solve integrals. Below are the tricks/techniques that I know for indefinite and definite integrals separately. ...

I have a question: Suppose $f$ is continuous and even on $[-a,a]$, $a>0$ then prove that $$\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$$ How can I do ...

I am in the last year of my school and studied integration this year I have done several Integration techniques like Integration By substitution By partial fractions By parts Trigo. substitutions ...

How would you compute for the definite integral of $$\int_0^{\infty}\frac{dx}{(1+x^2)^4}$$ I know that integral of $\displaystyle \frac1{(1+x^2)}$ equals $\tan^{-1}x$. I tried using integration by ...

$$ \int_2^4\frac{\sqrt{\log(9-x)}}{\sqrt{\log(9-x)}+\sqrt{\log(3+x)}}dx=1$$

The above integral appeared while trying to calculate the Fisher-information of a Cauchy-distributed sample in my statistics homework. I plugged it into Wolfram Alpha, which gives the answer $\frac \...

It was originally asked here. This was also asked here. I have faced some difficulties to do the following integral: $$ I=\int_{0}^{2\pi}d\phi\int_{0}^{\pi}d\theta~\sin\theta\int_{0}^{\infty}dr~r^2\...

How would you find $$\int \frac{1}{{(1+x^2)^3}} \ dx \ ?$$ I think it calls for some trig substitution, but I tried and it didn't work (or at least I couldn't see it how would work).

I've been reviewing my probability and statistics book and just got up to continuous distributions. The book defines the expected value of a continuous random variable as: $E[H(X)] = \int_{-\infty}^{\...

I'm learning to integrate and I'd like to hear what are you favorite integration tricks? I can't contribute much to this thread, but I like the fact that: $$\int_{-a}^{a}{f(x)}dx=0 \space\text{if}\...

I know that the value of the integral of $\cot(x)$ is $\log|\sin x|+C$ . But what about: $$\int\log(\sin x)~dx$$ Is there any easy way to find an antiderivative for this? Thanks.

While browsing MSE, I found some posts regarding integration tricks / integration formulae, for both definite and indefinite integrals. I saw this post, this post, this post, and some other posts. I ...

$\displaystyle\int_0^\frac{\pi}{2}\frac{1}{2-\cos x} \, dx$ using the substitution $t=\tan\frac{1}{2}x$ $x=2\tan^{-1}t$ $\dfrac{dx}{dt}=\dfrac{2}{1+t^2}$ $dx=\dfrac{2}{1+t^2}\,dt$ $\...