What is the integral of e^xsin(4x) ?

The integral of e^xsin(4x) is -(4e^xcos(4x))/(17)+(e^xsin(4x))/(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^xsin(4x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

Apply Integration By Parts

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

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

Therefore

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

Isolate

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

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

Add a constant to the solution

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

\frac{d}{d x} (lo g_{3} (4 x + 1))

\frac{\partial}{\partial y} (- 9 sin (3 x + yz))

x \to \frac{π}{8} lim (tan (24 x))

tan (8 x)

\int_{0}^{1} 9 \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

What is the integral of e^xsin(4x) ?
The integral of e^xsin(4x) is -(4e^xcos(4x))/(17)+(e^xsin(4x))/(17)+C