$\int\frac{1}{v\left(1+v^2\right)}dv$

$4x^6-64x^2$

$12m^2+48mn+48n^2$

$\frac{5x-15}{x-3}$

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

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

$2\int_0^a\left(\frac{1}{\left(a^2+x^2\right)^{\frac{3}{2}}}\right)dx$