Question

If \[\text{I}=\int e^{-x}\cos x\,dx\], which relation is obtained during integration by parts?

Options

• \[2\text{I}=(\sin x+\cos x)e^{-x}\]

• \[2\text{I}=(\cos x-\sin x)e^{x}\]

• \[\text{I}=(\sin x-\cos x)e^{-x}\]

• \[2\text{I}=(\sin x-\cos x)e^{-x}\]

Answer 1

Integration by parts returns the original integral \[\text{I}\] to the right-hand side. Collecting it gives \[2\text{I}=(\sin x-\cos x)e^{-x}\].