What is the integral of e^{20x}6sin(2x) ?

The integral of e^{20x}6sin(2x) is 6(-(e^{20x}cos(2x))/(202)+(5e^{20x}sin(2x))/(101))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{20x}6sin(2x)

\int e^{20 x} 6 sin (2 x) d x

6 (- \frac{e ^{20 x} cos ( 2 x )}{202} + \frac{5 e ^{20 x} sin ( 2 x )}{101}) + C

Solution steps

\int e^{20 x} \cdot 6 sin (2 x) d x

Take the constant out:

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

= 6 \cdot \int e^{20 x} sin (2 x) d x

Apply Integration By Parts

: - \frac{1}{2} e^{20 x} cos (2 x) - \int - 10 e^{20 x} cos (2 x) d x

= 6 (- \frac{1}{2} e^{20 x} cos (2 x) - \int - 10 e^{20 x} cos (2 x) d x)

Take the constant out:

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

= 6 (- \frac{1}{2} e^{20 x} cos (2 x) - (- 10 \cdot \int e^{20 x} cos (2 x) d x))

Apply Integration By Parts

: \frac{1}{2} e^{20 x} sin (2 x) - \int 10 e^{20 x} sin (2 x) d x

= 6 (- \frac{1}{2} e^{20 x} cos (2 x) - (- 10 (\frac{1}{2} e^{20 x} sin (2 x) - \int 10 e^{20 x} sin (2 x) d x)))

Take the constant out:

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

= 6 (- \frac{1}{2} e^{20 x} cos (2 x) - (- 10 (\frac{1}{2} e^{20 x} sin (2 x) - 10 \cdot \int e^{20 x} sin (2 x) d x)))

Therefore

6 \cdot \int e^{20 x} sin (2 x) d x = 6 (- \frac{1}{2} e^{20 x} cos (2 x) - (- 10 (\frac{1}{2} e^{20 x} sin (2 x) - 10 \cdot \int e^{20 x} sin (2 x) d x)))

Isolate

\int e^{20 x} sin (2 x) d x

= 6 (- \frac{e ^{20 x} cos ( 2 x )}{202} + \frac{5 e ^{20 x} sin ( 2 x )}{101})

Add a constant to the solution

= 6 (- \frac{e ^{20 x} cos ( 2 x )}{202} + \frac{5 e ^{20 x} sin ( 2 x )}{101}) + C

\int x \cdot sin (x) d x

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

\int 1 0^{4 x + 1} d x

\int 2 x e^{4 x^{2}} d x

\int 8 x e^{- 0.2 x} d x

What is the integral of e^{20x}6sin(2x) ?
The integral of e^{20x}6sin(2x) is 6(-(e^{20x}cos(2x))/(202)+(5e^{20x}sin(2x))/(101))+C