Integrate the function $\frac{x^3+x}{\left(x^4+2x^2+1\right)^5}$ from $-1$ to $1$

Evaluate the integral

$\int_9^4\left(\frac{x^2}{x+1}\right)dx$

Evaluate the integral

$\int_e^{\infty}\left(\frac{1}{x\left(\ln\left(x\right)\right)^3}\right)dx$

Evaluate the integral

$\int_2^{\infty}\left(\frac{lnx}{x}\right)dx$

Evaluate the integral

$\int_1^{25}\frac{\left(\left(lnx\right)^5\right)}{4x}dx$

Evaluate the integral

$\int_2^3\frac{1}{\sqrt{x-1}}dx$

Find the integral

$\int x\left(x^2-3\right)dx$

Evaluate the integral

$\int_0^1\left(\frac{ln\left(x\right)}{x}\right)dx$