 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/discrete-mathematics-continuous-mathematics-and-probability/4/a/solution

Let

I = \int e^{x} sin x d x

. Two applications of integration by parts give

I = e^{x} sin x - \int e^{x} cos x d x, \int e^{x} cos x d x = e^{x} cos x + I,

where additive constants can be absorbed at the end. Solving for

I

yields

\int e^{x} sin x d x = \frac{e ^{x}}{2} (sin x - cos x) + C .

Differentiating the answer gives

e^{x} sin x

 New to topics? Read the docs here!