Question

Integrate the function: $e^x(sinx+cosx)$

Answer 1

The correct answer is: $∴I=e^x sinx+C$
Let $I=∫e^x(sinx+cosx)dx$
Let $ƒ(x)=sinx$
$⧠ƒ'(x)=cosx$
$⧠I=∫e^x[{ƒ(x)+ƒ'(x)}]dx$
It is known that,$∫e^x[{ƒ(x)+ƒ'(x)}]dx=e^x ƒ(x)+C$
$∴I=e^x sinx+C$