What is the integral of 64e^{8x}sin(8x) ?

The integral of 64e^{8x}sin(8x) is 64((e^{8x}sin(8x))/(16)-(e^{8x}cos(8x))/(16))+C

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integral of 64e^{8x}sin(8x)

\int 64 e^{8 x} sin (8 x) d x

64 (\frac{e ^{8 x} sin ( 8 x )}{16} - \frac{e ^{8 x} cos ( 8 x )}{16}) + C

Solution steps

\int 64 e^{8 x} sin (8 x) d x

Take the constant out:

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

= 64 \cdot \int e^{8 x} sin (8 x) d x

Apply Integration By Parts

: - \frac{1}{8} e^{8 x} cos (8 x) - \int - e^{8 x} cos (8 x) d x

= 64 (- \frac{1}{8} e^{8 x} cos (8 x) - \int - e^{8 x} cos (8 x) d x)

Take the constant out:

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

= 64 (- \frac{1}{8} e^{8 x} cos (8 x) - (- \int e^{8 x} cos (8 x) d x))

Apply Integration By Parts

: \frac{1}{8} e^{8 x} sin (8 x) - \int e^{8 x} sin (8 x) d x

= 64 (- \frac{1}{8} e^{8 x} cos (8 x) - (- (\frac{1}{8} e^{8 x} sin (8 x) - \int e^{8 x} sin (8 x) d x)))

Therefore

64 \cdot \int e^{8 x} sin (8 x) d x = 64 (- \frac{1}{8} e^{8 x} cos (8 x) - (- (\frac{1}{8} e^{8 x} sin (8 x) - \int e^{8 x} sin (8 x) d x)))

Isolate

\int e^{8 x} sin (8 x) d x

= 64 (\frac{e ^{8 x} sin ( 8 x )}{16} - \frac{e ^{8 x} cos ( 8 x )}{16})

Add a constant to the solution

= 64 (\frac{e ^{8 x} sin ( 8 x )}{16} - \frac{e ^{8 x} cos ( 8 x )}{16}) + C

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What is the integral of 64e^{8x}sin(8x) ?
The integral of 64e^{8x}sin(8x) is 64((e^{8x}sin(8x))/(16)-(e^{8x}cos(8x))/(16))+C