Question

Evaluate $\int e^x(sinx+cosx)dx$.

Answer 1

$\int e^x(\sin x+\cos x)dx$

As we know that,

$\int e^x(f\left(x\right)+f^{\prime }\left(x\right))dx=e^{x}f\left(x\right)+C$

$\because \frac{d}{dx}\left(\sin x\right)=\cos x$

$\therefore \int e^x(\sin x+\cos x)dx=e^x\sin x+C$