$\frac{dy}{dx}=ln\:x\:-\:4x^2$

$1x^2-81$

$\int_0^{\infty}\left(\left(\frac{1}{a+b}\right)e^{\left(-\frac{x}{b}\right)}\cdot x\right)dx$

$\left(x-2y+3\right)dy+\left(2x+y-1\right)dx=0$

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

$\:cos^2x-sen^2x=2sen^2x-1$

$\frac{y^2}{y+5}=\frac{25}{y+5}$