What is the integral of-30e^{12t}sin(t) ?

The integral of-30e^{12t}sin(t) is -30(-(e^{12t}cos(t))/(145)+(12e^{12t}sin(t))/(145))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-30e^{12t}sin(t)

\int - 30 e^{12 t} sin (t) d t

- 30 (- \frac{e ^{12 t} cos ( t )}{145} + \frac{12 e ^{12 t} sin ( t )}{145}) + C

Solution steps

\int - 30 e^{12 t} sin (t) d t

Take the constant out:

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

= - 30 \cdot \int e^{12 t} sin (t) d t

Apply Integration By Parts

: - e^{12 t} cos (t) - \int - 12 e^{12 t} cos (t) d t

= - 30 (- e^{12 t} cos (t) - \int - 12 e^{12 t} cos (t) d t)

Take the constant out:

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

= - 30 (- e^{12 t} cos (t) - (- 12 \cdot \int e^{12 t} cos (t) d t))

Apply Integration By Parts

: e^{12 t} sin (t) - \int e^{12 t} \cdot 12 sin (t) d t

= - 30 (- e^{12 t} cos (t) - (- 12 (e^{12 t} sin (t) - \int e^{12 t} \cdot 12 sin (t) d t)))

Take the constant out:

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

= - 30 (- e^{12 t} cos (t) - (- 12 (e^{12 t} sin (t) - 12 \cdot \int e^{12 t} sin (t) d t)))

Therefore

- 30 \cdot \int e^{12 t} sin (t) d t = - 30 (- e^{12 t} cos (t) - (- 12 (e^{12 t} sin (t) - 12 \cdot \int e^{12 t} sin (t) d t)))

Isolate

\int e^{12 t} sin (t) d t

= - 30 (- \frac{e ^{12 t} cos ( t )}{145} + \frac{12 e ^{12 t} sin ( t )}{145})

Add a constant to the solution

= - 30 (- \frac{e ^{12 t} cos ( t )}{145} + \frac{12 e ^{12 t} sin ( t )}{145}) + C

\int \frac{4 x ^{3}}{25 + x ^{8}} d x

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

\int cos (π x) + 3 sin (\frac{x}{3}) d x

\int e^{4 x^{2}} 8 x d x

\int (cos (\frac{x}{2}) + sin (\frac{x}{2}))^{2} d x

What is the integral of-30e^{12t}sin(t) ?
The integral of-30e^{12t}sin(t) is -30(-(e^{12t}cos(t))/(145)+(12e^{12t}sin(t))/(145))+C