Solve the integral of logarithmic functions $\int x\cdot x\cdot x\cdot x\ln\left(x\right)dx$

Evaluate the limit

$\lim_{v\to\infty}\left(\frac{-x^3+6x^2-8x+1}{3x^2-7x^3+2x-3}\right)$

Evaluate the limit

$\lim_{x\to\infty}\left(\frac{\ln\left(x\right)}{\sqrt{x}}\right)$

Evaluate the limit

$\lim_{x\to\infty}\left(\frac{2x^3-2x^2+x-3}{x^3+2x^2-x+1}\right)$

Evaluate the limit

$\lim_{x\to\infty}\left(1-\frac{1}{x}\right)^x$

Evaluate the limit

$\lim_{x\to\infty}\left(1+\frac{2}{x}\right)^x$

Evaluate the limit

$\lim_{x\to\infty}\left(\frac{e^x}{x^2}\right)$

Evaluate the limit

$\lim_{x\to\infty}\left(x^{\frac{1}{x}}\right)$