Find the derivative using the quotient rule $\left(3+1\cdot -3xy\right)\left(3+4xy\right)$

Find the integral

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

Find the integral

$\int\frac{x}{\left(4x^2+3\right)^6}dx$

Find the integral

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

Find the integral

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

Find the integral

$\int\left(dx\div x^2\sqrt{9-x^2}\right)$

Find the integral

$\int\frac{x^2dx}{\left(9-x^2\right)^{\frac{3}{2}}}$

Find the integral

$\int\frac{dx}{x\sqrt{x^{2}+36}}$