What is the integral of e^{2x}sin(4x) ?

The integral of e^{2x}sin(4x) is -(e^{2x}cos(4x))/5+(e^{2x}sin(4x))/(10)+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(4x)

\int e^{2 x} sin (4 x) d x

- \frac{e ^{2 x} cos ( 4 x )}{5} + \frac{e ^{2 x} sin ( 4 x )}{10} + C

Solution steps

\int e^{2 x} sin (4 x) d x

Apply Integration By Parts

: - \frac{1}{4} e^{2 x} cos (4 x) - \int - \frac{1}{2} e^{2 x} cos (4 x) d x

= - \frac{1}{4} e^{2 x} cos (4 x) - \int - \frac{1}{2} e^{2 x} cos (4 x) d x

Take the constant out:

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

= - \frac{1}{4} e^{2 x} cos (4 x) - (- \frac{1}{2} \cdot \int e^{2 x} cos (4 x) d x)

Apply Integration By Parts

: \frac{1}{4} e^{2 x} sin (4 x) - \int \frac{1}{2} e^{2 x} sin (4 x) d x

= - \frac{1}{4} e^{2 x} cos (4 x) - (- \frac{1}{2} (\frac{1}{4} e^{2 x} sin (4 x) - \int \frac{1}{2} e^{2 x} sin (4 x) d x))

Take the constant out:

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

= - \frac{1}{4} e^{2 x} cos (4 x) - (- \frac{1}{2} (\frac{1}{4} e^{2 x} sin (4 x) - \frac{1}{2} \cdot \int e^{2 x} sin (4 x) d x))

Therefore

\int e^{2 x} sin (4 x) d x = - \frac{1}{4} e^{2 x} cos (4 x) - (- \frac{1}{2} (\frac{1}{4} e^{2 x} sin (4 x) - \frac{1}{2} \cdot \int e^{2 x} sin (4 x) d x))

Isolate

\int e^{2 x} sin (4 x) d x

= - \frac{e ^{2 x} cos ( 4 x )}{5} + \frac{e ^{2 x} sin ( 4 x )}{10}

Add a constant to the solution

= - \frac{e ^{2 x} cos ( 4 x )}{5} + \frac{e ^{2 x} sin ( 4 x )}{10} + C

\int_{0}^{4} \frac{x - 1}{x ^{2} - 4 x - 5} d x

\frac{\partial}{\partial x} (- x e^{x} sin (y))

f (x) = x^{2} + 91 x - 92, at x = 2

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

What is the integral of e^{2x}sin(4x) ?
The integral of e^{2x}sin(4x) is -(e^{2x}cos(4x))/5+(e^{2x}sin(4x))/(10)+C