What is the integral of sin(x)e^{-3x} ?

The integral of sin(x)e^{-3x} is -(e^{-3x}cos(x))/(10)-(3e^{-3x}sin(x))/(10)+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^{-3x}

\int sin (x) e^{- 3 x} d x

- \frac{e ^{- 3 x} cos ( x )}{10} - \frac{3 e ^{- 3 x} sin ( x )}{10} + C

Solution steps

\int sin (x) e^{- 3 x} d x

Apply Integration By Parts

: - e^{- 3 x} cos (x) - \int 3 e^{- 3 x} cos (x) d x

= - e^{- 3 x} cos (x) - \int 3 e^{- 3 x} cos (x) d x

Take the constant out:

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

= - e^{- 3 x} cos (x) - 3 \cdot \int e^{- 3 x} cos (x) d x

Apply Integration By Parts

: e^{- 3 x} sin (x) - \int - 3 e^{- 3 x} sin (x) d x

= - e^{- 3 x} cos (x) - 3 (e^{- 3 x} sin (x) - \int - 3 e^{- 3 x} sin (x) d x)

Take the constant out:

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

= - e^{- 3 x} cos (x) - 3 (e^{- 3 x} sin (x) - (- 3 \cdot \int e^{- 3 x} sin (x) d x))

Therefore

\int e^{- 3 x} sin (x) d x = - e^{- 3 x} cos (x) - 3 (e^{- 3 x} sin (x) - (- 3 \cdot \int e^{- 3 x} sin (x) d x))

Isolate

\int e^{- 3 x} sin (x) d x

= - \frac{e ^{- 3 x} cos ( x )}{10} - \frac{3 e ^{- 3 x} sin ( x )}{10}

Add a constant to the solution

= - \frac{e ^{- 3 x} cos ( x )}{10} - \frac{3 e ^{- 3 x} sin ( x )}{10} + C

\int \frac{x ^{2} + 2 x - 1}{x ^{3} + x ^{2} + x + 1} d x

\int \frac{2 x}{y ^{3}} d x

\int \frac{1}{8 x + 2} d x

\int \frac{1}{x ^{2}} cos (\frac{1}{x}) d x

\int (z + 1) e^{9 z} d z

What is the integral of sin(x)e^{-3x} ?
The integral of sin(x)e^{-3x} is -(e^{-3x}cos(x))/(10)-(3e^{-3x}sin(x))/(10)+C