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 e^{3 x} \cdot 3 sin (x) d x

= - e^{3 x} cos (x) - (- 3 (e^{3 x} sin (x) - \int e^{3 x} \cdot 3 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 x^{2} cos (\frac{1}{9} x) d x

\frac{d}{d x} (sec (x) tan^{2} (x))

\frac{\partial}{\partial x} (\frac{x ^{2} - y}{x ^{2} + y})

\int \frac{8 cosh ( x )}{x} d x

\int \frac{( 5 - x )}{2 x ^{2} + x - 1} d x

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