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

$\int\frac{5x^2+3x-1}{\left(1+x^2\right)\left(x-2\right)}dx$

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

$\left(2a^4+3b\right)\left(2a^4-3b\right)$

$ex^5-ex$

$\log\left(a\right)-3\log\left(b\right)+\frac{1}{4}\log\left(c\right)-\log\left(d\right)+\log\left(g+2\right)$