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

$cos^2b\:-\:sin^2b\:=\:2cos^2b\:-\:1$

$\left(3x+4\right)\left(3x-4\right)^2$

$2z^2+8z$

$\int\left(\frac{sin\left(3\sqrt{x}\right)}{2\sqrt{x}}\right)dx$

$y\left(1-x^2\right)dy=\left(y+1\right)^2dx$

$\sin^2\left(x\right)+\frac{3}{2}=1$