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

The integral of e^{8x}sin(x) is -(e^{8x}cos(x))/(65)+(8e^{8x}sin(x))/(65)+C

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

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

- \frac{e ^{8 x} cos ( x )}{65} + \frac{8 e ^{8 x} sin ( x )}{65} + C

Solution steps

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

Apply Integration By Parts

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

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

Take the constant out:

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

= - e^{8 x} cos (x) - (- 8 \cdot \int e^{8 x} cos (x) d x)

Apply Integration By Parts

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

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

Take the constant out:

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

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

Therefore

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

Isolate

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

= - \frac{e ^{8 x} cos ( x )}{65} + \frac{8 e ^{8 x} sin ( x )}{65}

Add a constant to the solution

= - \frac{e ^{8 x} cos ( x )}{65} + \frac{8 e ^{8 x} sin ( x )}{65} + C

\frac{\partial}{\partial x} (x^{2} sin (\frac{1}{x}))

\frac{1}{x ( x + 1 )}

\int \frac{3 x ^{2} + 4 x + 1}{3 x ^{3} + 6 x ^{2} + 3 x + 5} d x

y = x^{2} sin^{6} (x) + x cos^{- 4} (x)

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

What is the integral of e^{8x}sin(x) ?
The integral of e^{8x}sin(x) is -(e^{8x}cos(x))/(65)+(8e^{8x}sin(x))/(65)+C