What is the integral of e^{7x}sin(3x) ?

The integral of e^{7x}sin(3x) is -(3e^{7x}cos(3x))/(58)+(7e^{7x}sin(3x))/(58)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{7x}sin(3x)

\int e^{7 x} sin (3 x) d x

- \frac{3 e ^{7 x} cos ( 3 x )}{58} + \frac{7 e ^{7 x} sin ( 3 x )}{58} + C

Solution steps

\int e^{7 x} sin (3 x) d x

Apply Integration By Parts

: - \frac{1}{3} e^{7 x} cos (3 x) - \int - \frac{7}{3} e^{7 x} cos (3 x) d x

= - \frac{1}{3} e^{7 x} cos (3 x) - \int - \frac{7}{3} e^{7 x} cos (3 x) d x

Take the constant out:

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

= - \frac{1}{3} e^{7 x} cos (3 x) - (- \frac{7}{3} \cdot \int e^{7 x} cos (3 x) d x)

Apply Integration By Parts

: \frac{1}{3} e^{7 x} sin (3 x) - \int \frac{7}{3} e^{7 x} sin (3 x) d x

= - \frac{1}{3} e^{7 x} cos (3 x) - (- \frac{7}{3} (\frac{1}{3} e^{7 x} sin (3 x) - \int \frac{7}{3} e^{7 x} sin (3 x) d x))

Take the constant out:

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

= - \frac{1}{3} e^{7 x} cos (3 x) - (- \frac{7}{3} (\frac{1}{3} e^{7 x} sin (3 x) - \frac{7}{3} \cdot \int e^{7 x} sin (3 x) d x))

Therefore

\int e^{7 x} sin (3 x) d x = - \frac{1}{3} e^{7 x} cos (3 x) - (- \frac{7}{3} (\frac{1}{3} e^{7 x} sin (3 x) - \frac{7}{3} \cdot \int e^{7 x} sin (3 x) d x))

Isolate

\int e^{7 x} sin (3 x) d x

= - \frac{3 e ^{7 x} cos ( 3 x )}{58} + \frac{7 e ^{7 x} sin ( 3 x )}{58}

Add a constant to the solution

= - \frac{3 e ^{7 x} cos ( 3 x )}{58} + \frac{7 e ^{7 x} sin ( 3 x )}{58} + C

\int 8 tan^{3} (x) sec (x) d x

\frac{d}{d x} (3 x^{2} - 10)

x^{2} y^{^{''}} - 7 x y^{^{'}} + 15 y = 0, y (1) = 0, y^{^{'}} (1) = 2

\frac{d}{d x} (\frac{x}{x ^{4} + 4})

\frac{d}{d x} (\frac{x ^{4}}{5 - x ^{3}})

What is the integral of e^{7x}sin(3x) ?
The integral of e^{7x}sin(3x) is -(3e^{7x}cos(3x))/(58)+(7e^{7x}sin(3x))/(58)+C