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

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

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) - (- \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)))

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

Add a constant to the solution

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

\int x \cdot 2 x + 1 d x

x \to 0 lim (\frac{3 ( 3 - x ) - 9}{x})

f (x) = x^{\frac{9}{2}} e^{x}

(- 2, - 6), (0, 6)

\int (6 x) d x

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