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

The integral of-e^{2x}cos(x) is -1/5 e^{2x}sin(x)-2/5 e^{2x}cos(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-e^{2x}cos(x)

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

- \frac{1}{5} e^{2 x} sin (x) - \frac{2}{5} e^{2 x} cos (x) + C

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

Take the constant out:

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

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

Therefore

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

Isolate

\int e^{2 x} cos (x) d x

= - (\frac{e ^{2 x} sin ( x )}{5} + \frac{2 e ^{2 x} cos ( x )}{5})

Simplify

- (\frac{e ^{2 x} sin ( x )}{5} + \frac{2 e ^{2 x} cos ( x )}{5}) : - \frac{1}{5} e^{2 x} sin (x) - \frac{2}{5} e^{2 x} cos (x)

= - \frac{1}{5} e^{2 x} sin (x) - \frac{2}{5} e^{2 x} cos (x)

Add a constant to the solution

= - \frac{1}{5} e^{2 x} sin (x) - \frac{2}{5} e^{2 x} cos (x) + C

\int (ln (cos (x))) d x

\int \frac{x - 9}{4 x ^{2} + 3 x - 1} d x

\int (7 y^{6} + 8 y^{3} - 1) d y

\int \frac{4}{9 - x ^{2}} d x

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

What is the integral of-e^{2x}cos(x) ?
The integral of-e^{2x}cos(x) is -1/5 e^{2x}sin(x)-2/5 e^{2x}cos(x)+C