$2\ln\left(3e^{2x}\right)+3\ln\left(2e^{4x}\right)$

$sin\left(3x+5y\right)-sin\left(3x-5y\right)$

$x^2-10x=-5$

$\sin\left(12x\right)=\sqrt{2}\cos\left(6x\right)$

$75x^2+45x+27$

$\int\left(t\:\:\ln\:t\right)\:^2dt$

$\int\frac{4x-1}{\left(x+4\right)\left(x-2\right)\left(x+3\right)}dx$