What is the integral of e^{5x+3}sin(2x-1) ?

The integral of e^{5x+3}sin(2x-1) is -(2e^{5x+3}cos(2x-1))/(29)+(5e^{5x+3}sin(2x-1))/(29)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{5x+3}sin(2x-1)

\int e^{5 x + 3} sin (2 x - 1) d x

- \frac{2 e ^{5 x + 3} cos ( 2 x - 1 )}{29} + \frac{5 e ^{5 x + 3} sin ( 2 x - 1 )}{29} + C

Solution steps

\int e^{5 x + 3} sin (2 x - 1) d x

Apply Integration By Parts

: - \frac{1}{2} e^{5 x + 3} cos (2 x - 1) - \int - \frac{5}{2} e^{5 x + 3} cos (2 x - 1) d x

= - \frac{1}{2} e^{5 x + 3} cos (2 x - 1) - \int - \frac{5}{2} e^{5 x + 3} cos (2 x - 1) d x

Take the constant out:

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

= - \frac{1}{2} e^{5 x + 3} cos (2 x - 1) - (- \frac{5}{2} \cdot \int e^{5 x + 3} cos (2 x - 1) d x)

Apply Integration By Parts

: \frac{1}{2} e^{5 x + 3} sin (2 x - 1) - \int \frac{5}{2} e^{5 x + 3} sin (2 x - 1) d x

= - \frac{1}{2} e^{5 x + 3} cos (2 x - 1) - (- \frac{5}{2} (\frac{1}{2} e^{5 x + 3} sin (2 x - 1) - \int \frac{5}{2} e^{5 x + 3} sin (2 x - 1) d x))

Take the constant out:

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

= - \frac{1}{2} e^{5 x + 3} cos (2 x - 1) - (- \frac{5}{2} (\frac{1}{2} e^{5 x + 3} sin (2 x - 1) - \frac{5}{2} \cdot \int e^{5 x + 3} sin (2 x - 1) d x))

Therefore

\int e^{5 x + 3} sin (2 x - 1) d x = - \frac{1}{2} e^{5 x + 3} cos (2 x - 1) - (- \frac{5}{2} (\frac{1}{2} e^{5 x + 3} sin (2 x - 1) - \frac{5}{2} \cdot \int e^{5 x + 3} sin (2 x - 1) d x))

Isolate

\int e^{5 x + 3} sin (2 x - 1) d x

= - \frac{2 e ^{5 x + 3} cos ( 2 x - 1 )}{29} + \frac{5 e ^{5 x + 3} sin ( 2 x - 1 )}{29}

Add a constant to the solution

= - \frac{2 e ^{5 x + 3} cos ( 2 x - 1 )}{29} + \frac{5 e ^{5 x + 3} sin ( 2 x - 1 )}{29} + C

\int sec (4 x) - csc (\frac{2 x}{3}) d x

\int \frac{1}{2 - 3 y} d y

\int sin (a \cdot x) \cdot sin (b \cdot x) d x

\int \frac{r}{16 - 9 r ^{2}} d r

\int \frac{100}{25 x ^{2} + 36} d x

What is the integral of e^{5x+3}sin(2x-1) ?
The integral of e^{5x+3}sin(2x-1) is -(2e^{5x+3}cos(2x-1))/(29)+(5e^{5x+3}sin(2x-1))/(29)+C