Solve $\int\left(\ln5x+2e^{2x}\right)\,dx$ $$\int\left(\ln(5x)+2e^{2x}\right)\,dx$$
I am not getting how to integrate this function. Please help.
You have
$$\int (\ln 5x + e^{2x})~dx = \int \ln 5x~dx + \int 2e^{2x}~dx = I_1 + I_2.$$
For $I_2$ try by subtstitution and for $I_1$ try by parts with $u = \ln 5x$ and $v' = 1$.
Doing it by parts and splitting, We get $\int\left(\ln(5x)+2e^{2x}\right)\,dx=\boxed{x\ln \left(5x\right)-x+e^{2x}+C}$