$\lim_{x\to0}\left(\frac{e^x-1}{3x^2+5}\right)$

$10\left(t+1\right)\left(\frac{dy}{dt}\right)-9y=9t$

$\int\left(x^2+1\right)x^2dx$

$\int\left(\frac{\csc\left(x\right)-2\sec\left(x\right)}{\sin^2\left(x\right)\csc\left(x\right)}\right)dx$

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

$\int\left(\frac{2x^3-4x^2-15x+5}{x^2-2x-3}\right)dx$

$\frac{8a^{12}-729}{2a^4+9}$