$\lim_{x\to\infty}\left(\frac{-4ln\left(x^5\right)}{\sqrt[3]{5x+19}}\right)$

$\lim_{x\to0}\left(\frac{2\sin\left(x^2\right)}{1-\cos\left(x\right)}\right)$

$2\sqrt{1-x}=\sqrt{16-3x}-1$

$\int\frac{ln\:2x^3}{x}dx$

$\int\left(2x^5+3\right)\ln\left(x\right)dx$

$-5+8z+24-17z$

$2\sec\left(x\right)\csc\left(x\right)$