What is the integral of sin(x)(e^x) ?

The integral of sin(x)(e^x) is -(e^xcos(x))/2+(e^xsin(x))/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(x)(e^x)

\int sin (x) (e^{x}) d x

- \frac{e ^{x} cos ( x )}{2} + \frac{e ^{x} sin ( x )}{2} + C

Solution steps

\int sin (x) e^{x} d x

Apply Integration By Parts

: - e^{x} cos (x) - \int - e^{x} cos (x) d x

= - e^{x} cos (x) - \int - e^{x} cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - e^{x} cos (x) - (- \int e^{x} cos (x) d x)

Apply Integration By Parts

: e^{x} sin (x) - \int e^{x} sin (x) d x

= - e^{x} cos (x) - (- (e^{x} sin (x) - \int e^{x} sin (x) d x))

Therefore

\int e^{x} sin (x) d x = - e^{x} cos (x) - (- (e^{x} sin (x) - \int e^{x} sin (x) d x))

Isolate

\int e^{x} sin (x) d x

= - \frac{e ^{x} cos ( x )}{2} + \frac{e ^{x} sin ( x )}{2}

Add a constant to the solution

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

\int \frac{4 x}{2 x ^{2} + 5} d x

\int 7 tan (3 x) ln (cos (3 x)) d x

\int \frac{- 1 - x}{- x ^{2} - 1} d x

\int t e^{\frac{t}{2}} d t

\int (3 csc^{2} (x) - 5 sec (x) tan (x)) d x

What is the integral of sin(x)(e^x) ?
The integral of sin(x)(e^x) is -(e^xcos(x))/2+(e^xsin(x))/2+C