$\int\left(\frac{3x^2}{1-3x^2}\right)dx$

$2\tan\left(u\right)^2-\sec\left(u\right)^2$

$\:\frac{x}{3x+1}=\frac{x-1}{2x+3}$

$\frac{cot^3x\left(cot^2x-csc^2x\right)}{-tan\left(x\right)}$

$\int_a^{3x^3}x^2dx$

$5cos2x=2$

$\frac{sin\left(x+3y\right)+sin\left(3x+y\right)}{sin2x+sin2y}$