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

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

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

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

Solution steps

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

Therefore

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

Isolate

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

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

Add a constant to the solution

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

\int \frac{16 x ^{2} - 48 x + 15}{2 x ^{3} - 7 x ^{2} + 3 x} d x

e^{0}

\int z 1 - z d z

x \to 0 lim (\frac{x - 2}{∣ x - 2 ∣})

\int_{0}^{4} y - y + 2 d y

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