$\frac{dy}{dt}=\frac{3}{xe^{t+7x}}$

$\int2\sqrt{5+4x-x^2}dx$

$\left(x^2+3\right)\left(x+2\right)\left(x+4\right)$

$\int\arctan\left(x^{10}\right)dx$

$\:\int_{\frac{3\pi}{2}}^{2\pi}x\:\sin\left(\frac{x}{2}\right)dx$

$\sin^2x\cdot\sec^2x$

$\left(\frac{4}{3}m^5x^2+\frac{7}{3}n^4y^2\right)^2$