Integrals — Class 12 Maths Solution

Let $I = \int {{e^x}\left( {\sin x + \cos x} \right)dx}$

Put ${e^x}\sin x = t$ $\Rightarrow$ $\left( {{e^x}\cos x + \sin x{e^x}} \right)dx = dt$

$\Rightarrow$ ${e^x}\left( {\sin x + \cos x} \right)dx = dt$

$\therefore$ $I = \int {dt} = t + C = {e^x}\sin x + C$