What is the integral of e^{-4x}cos(x) ?

The integral of e^{-4x}cos(x) is (e^{-4x}sin(x))/(17)-(4e^{-4x}cos(x))/(17)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{-4x}cos(x)

\int e^{- 4 x} cos (x) d x

\frac{e ^{- 4 x} sin ( x )}{17} - \frac{4 e ^{- 4 x} cos ( x )}{17} + C

Solution steps

\int e^{- 4 x} cos (x) d x

Apply Integration By Parts

: e^{- 4 x} sin (x) - \int - 4 e^{- 4 x} sin (x) d x

= e^{- 4 x} sin (x) - \int - 4 e^{- 4 x} sin (x) d x

Take the constant out:

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

= e^{- 4 x} sin (x) - (- 4 \cdot \int e^{- 4 x} sin (x) d x)

Apply Integration By Parts

: - e^{- 4 x} cos (x) - \int 4 e^{- 4 x} cos (x) d x

= e^{- 4 x} sin (x) - (- 4 (- e^{- 4 x} cos (x) - \int 4 e^{- 4 x} cos (x) d x))

Take the constant out:

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

= e^{- 4 x} sin (x) - (- 4 (- e^{- 4 x} cos (x) - 4 \cdot \int e^{- 4 x} cos (x) d x))

Therefore

\int e^{- 4 x} cos (x) d x = e^{- 4 x} sin (x) - (- 4 (- e^{- 4 x} cos (x) - 4 \cdot \int e^{- 4 x} cos (x) d x))

Isolate

\int e^{- 4 x} cos (x) d x

= \frac{e ^{- 4 x} sin ( x )}{17} - \frac{4 e ^{- 4 x} cos ( x )}{17}

Add a constant to the solution

= \frac{e ^{- 4 x} sin ( x )}{17} - \frac{4 e ^{- 4 x} cos ( x )}{17} + C

\int \frac{1}{x ^{4} x ^{2} - 16} d x

\int x^{4} - 10 x^{2} + 25 d x

\int y sin (2 y) d y

\int sec^{13} (2 θ) tan^{3} (2 θ) d θ

\int \frac{1}{( y + 1 ) ln ( y + 1 )} d y

What is the integral of e^{-4x}cos(x) ?
The integral of e^{-4x}cos(x) is (e^{-4x}sin(x))/(17)-(4e^{-4x}cos(x))/(17)+C