Question

The integral of $\int e^x(\sin x+\cos x)dx$ is

• A. $e^x\cos x+c$
• B. $e^x\sin x+c$
• C. $e^x\sec x+c$
• D. none of this

Answer 1

The correct option is B $e^x\sin x+c$

Now,

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

$=\int e^x\sin xdx$$+\int e^x\cos xdx$

$=e^x\left(\sin x\right)-\int \left(\cos x\right).e^{x}dx$$+\int e^x\cos xdx$

$=e^x\left(\sin x\right)+c$ [ Where $c$ is integrating constant]