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

$18x^2+27x-36$

$\log_{4}\left(x+3\right)=2$

$\int_1^{\infty}\frac{13}{8x\left(x+1\right)^2}dx$

$sin\left(x\right)sec\left(x\right)=\frac{1}{cot\left(x\right)}$

$\lim_{x\to\pi}\left(\left(\pi-x\right)\tan\left(\frac{x}{2}\right)\right)$

$\frac{dy}{dx}=\frac{204x\:-\:459}{\left(-4x+9\right)y}$