What is the integral of e^{3x}sin(4x) ?

The integral of e^{3x}sin(4x) is -(4e^{3x}cos(4x))/(25)+(3e^{3x}sin(4x))/(25)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{3x}sin(4x)

\int e^{3 x} sin (4 x) d x

- \frac{4 e ^{3 x} cos ( 4 x )}{25} + \frac{3 e ^{3 x} sin ( 4 x )}{25} + C

Solution steps

\int e^{3 x} sin (4 x) d x

Apply Integration By Parts

= - \frac{1}{4} e^{3 x} cos (4 x) - \int - \frac{3}{4} e^{3 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^{3 x} cos (4 x) - (- \frac{3}{4} \cdot \int e^{3 x} cos (4 x) d x)

Apply Integration By Parts

= - \frac{1}{4} e^{3 x} cos (4 x) - (- \frac{3}{4} (\frac{1}{4} e^{3 x} sin (4 x) - \int \frac{3}{4} e^{3 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^{3 x} cos (4 x) - (- \frac{3}{4} (\frac{1}{4} e^{3 x} sin (4 x) - \frac{3}{4} \cdot \int e^{3 x} sin (4 x) d x))

Therefore

\int e^{3 x} sin (4 x) d x = - \frac{1}{4} e^{3 x} cos (4 x) - (- \frac{3}{4} (\frac{1}{4} e^{3 x} sin (4 x) - \frac{3}{4} \cdot \int e^{3 x} sin (4 x) d x))

Isolate

\int e^{3 x} sin (4 x) d x

= - \frac{4 e ^{3 x} cos ( 4 x )}{25} + \frac{3 e ^{3 x} sin ( 4 x )}{25}

Add a constant to the solution

= - \frac{4 e ^{3 x} cos ( 4 x )}{25} + \frac{3 e ^{3 x} sin ( 4 x )}{25} + C

x^{2} y^{^{''}} - 2 x y^{^{'}} + 2 y = 4 x^{2}

csc^{7} (2 t^{π} + π^{3})

x \to 6 - lim (f (x))

\int x \cdot x d x

\int \frac{1}{e ^{\frac{x}{a}} - e ^{- \frac{x}{a}}} d x

What is the integral of e^{3x}sin(4x) ?
The integral of e^{3x}sin(4x) is -(4e^{3x}cos(4x))/(25)+(3e^{3x}sin(4x))/(25)+C