What is the integral of e^{-7x}sin(2x) ?

The integral of e^{-7x}sin(2x) is -(2e^{-7x}cos(2x))/(53)-(7e^{-7x}sin(2x))/(53)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{-7x}sin(2x)

\int e^{- 7 x} sin (2 x) d x

- \frac{2 e ^{- 7 x} cos ( 2 x )}{53} - \frac{7 e ^{- 7 x} sin ( 2 x )}{53} + C

Solution steps

\int e^{- 7 x} sin (2 x) d x

Apply Integration By Parts

: - \frac{1}{2} e^{- 7 x} cos (2 x) - \int \frac{7}{2} e^{- 7 x} cos (2 x) d x

= - \frac{1}{2} e^{- 7 x} cos (2 x) - \int \frac{7}{2} e^{- 7 x} cos (2 x) d x

Take the constant out:

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

= - \frac{1}{2} e^{- 7 x} cos (2 x) - \frac{7}{2} \cdot \int e^{- 7 x} cos (2 x) d x

Apply Integration By Parts

: \frac{1}{2} e^{- 7 x} sin (2 x) - \int - \frac{7}{2} e^{- 7 x} sin (2 x) d x

= - \frac{1}{2} e^{- 7 x} cos (2 x) - \frac{7}{2} (\frac{1}{2} e^{- 7 x} sin (2 x) - \int - \frac{7}{2} e^{- 7 x} sin (2 x) d x)

Take the constant out:

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

= - \frac{1}{2} e^{- 7 x} cos (2 x) - \frac{7}{2} (\frac{1}{2} e^{- 7 x} sin (2 x) - (- \frac{7}{2} \cdot \int e^{- 7 x} sin (2 x) d x))

Therefore

\int e^{- 7 x} sin (2 x) d x = - \frac{1}{2} e^{- 7 x} cos (2 x) - \frac{7}{2} (\frac{1}{2} e^{- 7 x} sin (2 x) - (- \frac{7}{2} \cdot \int e^{- 7 x} sin (2 x) d x))

Isolate

\int e^{- 7 x} sin (2 x) d x

= - \frac{2 e ^{- 7 x} cos ( 2 x )}{53} - \frac{7 e ^{- 7 x} sin ( 2 x )}{53}

Add a constant to the solution

= - \frac{2 e ^{- 7 x} cos ( 2 x )}{53} - \frac{7 e ^{- 7 x} sin ( 2 x )}{53} + C

\int e^{2 z} cos (\frac{1}{4} z) d z

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

\int (tan^{3} (2 x)) (sec^{3} (2 x)) (1) d x

\int \frac{3 x}{x ^{2} + 10 x + 30} d x

\int \frac{x ^{3} + x + 1}{x ^{2} + 4} d x

What is the integral of e^{-7x}sin(2x) ?
The integral of e^{-7x}sin(2x) is -(2e^{-7x}cos(2x))/(53)-(7e^{-7x}sin(2x))/(53)+C