Integrals of Trigonometric Functions and Exponentials

Indefinite integrals of products of an exponential and a trigonometric function.

\int e^{x} sin x d x = \frac{1}{2} e^{x} (sin x - cos x) + C

\int e^{b x} sin a x d x = \frac{1}{a ^{2} + b ^{2}} e^{b x} (b sin a x - a cos a x) + C

\int e^{x} cos x d x = \frac{1}{2} e^{x} (sin x + cos x) + C

\int e^{b x} cos a x d x = \frac{1}{a ^{2} + b ^{2}} e^{b x} (a sin a x + b cos a x) + C

\int x e^{x} sin x d x = \frac{1}{2} e^{x} (cos x - x cos x + x sin x) + C

\int x e^{x} cos x d x = \frac{1}{2} e^{x} (x cos x - sin x + x sin x) + C