$\int5xln\left(1+x\right)dx$

$\int\left(7-2x\right)^3.e^{\frac{x}{4}}dx$

$\frac{dy}{dx}=\frac{1}{15}\left(4+3x\right)^5+c$

$xy'+y=\frac{\left(2+y\right)}{\left(5-2y\right)}$

$\lim\:_{x\to\:1}\left(2^x+x\right)^{\frac{1}{x}}+\lim\:_{x\to\:0}\left(\frac{cos\left(x-1\right)}{x}\right)$

$\frac{tanx}{1+tanx}=\frac{sinx}{sinx\:+\:cosx}$

$\frac{12x}{8y}$