Find the limit of $\frac{-x^3+6x^2-8x+1}{3x^2-7x^3+2x-3}$ as $x$ approaches $\infty $

Compute the integral

$\int\ln\left(x\right)dx$

Compute the integral

$\int\cos\left(4x\right)\cdot\cos\left(6x\right)dx$

Compute the integral

$\int\sec\left(5x\right)\cdot\tan\left(5x\right)dx$

Compute the integral

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

Compute the integral

$\int\csc\left(x\right)dx$

Compute the integral

$\int\ln\left(x+1\right)dx$

Compute the integral

$\int\sin\left(4x\right)\cdot\cos\left(2x\right)dx$