What is the integral of 36e^{-6x}sin(6x) ?

The integral of 36e^{-6x}sin(6x) is 36(-(e^{-6x}cos(6x))/(12)-(e^{-6x}sin(6x))/(12))+C

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integral of 36e^{-6x}sin(6x)

\int 36 e^{- 6 x} sin (6 x) d x

36 (- \frac{e ^{- 6 x} cos ( 6 x )}{12} - \frac{e ^{- 6 x} sin ( 6 x )}{12}) + C

Solution steps

\int 36 e^{- 6 x} sin (6 x) d x

Take the constant out:

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

= 36 \cdot \int e^{- 6 x} sin (6 x) d x

Apply Integration By Parts

: - \frac{1}{6} e^{- 6 x} cos (6 x) - \int e^{- 6 x} cos (6 x) d x

= 36 (- \frac{1}{6} e^{- 6 x} cos (6 x) - \int e^{- 6 x} cos (6 x) d x)

Apply Integration By Parts

: \frac{1}{6} e^{- 6 x} sin (6 x) - \int - e^{- 6 x} sin (6 x) d x

= 36 (- \frac{1}{6} e^{- 6 x} cos (6 x) - (\frac{1}{6} e^{- 6 x} sin (6 x) - \int - e^{- 6 x} sin (6 x) d x))

Take the constant out:

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

= 36 (- \frac{1}{6} e^{- 6 x} cos (6 x) - (\frac{1}{6} e^{- 6 x} sin (6 x) - (- \int e^{- 6 x} sin (6 x) d x)))

Therefore

36 \cdot \int e^{- 6 x} sin (6 x) d x = 36 (- \frac{1}{6} e^{- 6 x} cos (6 x) - (\frac{1}{6} e^{- 6 x} sin (6 x) - (- \int e^{- 6 x} sin (6 x) d x)))

Isolate

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

= 36 (- \frac{e ^{- 6 x} cos ( 6 x )}{12} - \frac{e ^{- 6 x} sin ( 6 x )}{12})

Add a constant to the solution

= 36 (- \frac{e ^{- 6 x} cos ( 6 x )}{12} - \frac{e ^{- 6 x} sin ( 6 x )}{12}) + C

\int (x - 2) (x^{2} - 4 x + 9) d x

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

\frac{\partial}{\partial s} (s t)

x^{4} - 2 x^{3} + 5

\int_{0}^{t} x d x

What is the integral of 36e^{-6x}sin(6x) ?
The integral of 36e^{-6x}sin(6x) is 36(-(e^{-6x}cos(6x))/(12)-(e^{-6x}sin(6x))/(12))+C