Question

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

Answer 1

$$\begin{gathered} \mathrm{Let}I=\int e^{2x}\left(-\sin x+2\cos x\right)dx \\ \mathrm{Put}{e}^{2x}\cos x=t \\ \mathrm{Diff}\mathrm{both}\mathrm{sides}\mathrm{w}.\mathrm{r}.\mathrm{t}x \\ \left[2e^{2x}\cos x+e^{2x}\times \left(-\sin x\right)\right]dx=dt \\ \therefore I=\int dt \\ =t+C \\ =e^{2x}\cos x+C \end{gathered}$$