$\int\:\:csc\:\pi\:\:x\:cot\:\pi\:\:x\:dx$

$\int3\left(y^6-4y^{-3}\right)\left(y^7+14y^{-2}-7\right)^6dx$

$\left(4m^5+8y\right)\left(4m^5-8y\right)$

$\int-3x^2e^{4x}dx$

$cos\:2x=cos^4x-sin^4x$

$\left(y^2+y+1\right)\left(y^2-y-1\right)$

$y\left(1+y\right)-3y^2-\left(y+1\right)$