Find the integral $\int\frac{x+4}{\left(x+1\right)^2}dx$

Find the integral

$\int\frac{dx}{\sqrt{25-9x^2}}$

Find the integral

$\int\frac{\sqrt{x^2+4}}{x^4}dx$

Find the integral

$\int\frac{x}{\sqrt{49+x^2}}dx$

Find the integral

$\int\frac{dx}{\left(5-4x-x^2\right)^{\frac{3}{2}}}$

Find the integral

$\int\frac{\left(3x-5\right)}{\left(x-1\right)\left(x^2-1\right)}dx$

Find the integral

$\int\frac{3x-5}{\left(x-1\right)\left(x^2-1\right)}dx$

Find the integral

$\int\frac{x^2}{\sqrt{4+x^2}}dx$