Linked Questions

My title is pretty vague, so let me elaborate on what exactly it is that I am looking for. I came across this integral $$ \int \frac{x \sin x }{1 + \cos^{2}x } dx $$ Now, I know that this indefinite ...

$\int \frac{dx}{\left(x^2+a^2\right)^3}$. I tried to use partial method were $u\:=\frac{1}{\left(x^2+a^2\right)^3}$ and dv = dx but got no result.

$$ \int \frac{dx}{\left(x^2+9\right)^2}$$ How would you solve this with partial integration (without trigonometry)?

Find $$I_n(a)=\displaystyle \int \limits_0^1 \dfrac{dx}{(x^2+a^2)^n}, \, a\ne0, \, 0\ne n \in \mathbb{N}.$$ I have following ideas. We have $I_n(a)=I_n(-a)$. \begin{align} \forall \,0\ne n \in \mathbb{...

I am not sure if Mathematics Stack Exchange allows this kind of questions. But I do think there are some who can guide me through this. I am working on Indefinite Integrals for quite a long time and ...

My textbook says that any rational function can be integrated using partial fraction expansion. So I was eager to try this out. But I got stuck with my very first example. How do I integrate $\frac{8x^...

Are there any integration methodologies to find antiderivatives of functions, other than integration by parts/substitution? General methods are preferred, but some methods that can be applied to ...