Question

Integrate $\int e^{\sin x}.\cos xdx$

Answer 1

$I=\int e^{sinx}.cosx.dx$

Put $sinx=t$

differentiating $cosxdx=dt$

$I=\int e^t.dt$ $\because \int e^{x}dx=e^x+c$

$I=e^t+c$

$I=e^{sinx}+c$