$\left(\frac{2x^{-3}y^6}{x^2y^{-4}}\right)^2$

$\frac{dy}{dx}=3x^2\left(y^2+1\right)\:\:\:\:\:\:\:\:\:\:$

$\int\left(\frac{x+4}{x^2+8x+35}\right)dx$

$2x^2+8xy+4xy^2$

$\int\left(x+4\right)^7\left(x+5\right)dx$

$\lim_{x\to0}\left(\frac{sinx-x}{sinx+x}\right)$

$\log_a\left(\frac{b}{c}\right)+\log_a\left(b\right)$