Question

$\int e^x$ (sin x + cos x)dx is equal to -

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Whenever you come across an integral which has $e^x$ with some other function in its integrand, it is advised to check whether the integral is of the form of $\int e^x$ [f(x) + f'(x)]dx. In that case, we can use the formula $\int e^x$ [f(x) + f'(x)]dx = $e^x$ f(x).

Here, we can see that cos x is the derivative of sin x, so the given integral is of the form $\int e^x$ [f(x) + f'(x)]dx. Hence we can directly say that the solution of this would be $e^x$ sin x + C.