What is the integral of e^{4x}sin(6x) ?

The integral of e^{4x}sin(6x) is -(3e^{4x}cos(6x))/(26)+(e^{4x}sin(6x))/(13)+C

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integral of e^{4x}sin(6x)

\int e^{4 x} sin (6 x) d x

- \frac{3 e ^{4 x} cos ( 6 x )}{26} + \frac{e ^{4 x} sin ( 6 x )}{13} + C

Solution steps

\int e^{4 x} sin (6 x) d x

Apply Integration By Parts

: - \frac{1}{6} e^{4 x} cos (6 x) - \int - \frac{2}{3} e^{4 x} cos (6 x) d x

= - \frac{1}{6} e^{4 x} cos (6 x) - \int - \frac{2}{3} e^{4 x} cos (6 x) d x

Take the constant out:

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

= - \frac{1}{6} e^{4 x} cos (6 x) - (- \frac{2}{3} \cdot \int e^{4 x} cos (6 x) d x)

Apply Integration By Parts

: \frac{1}{6} e^{4 x} sin (6 x) - \int \frac{2}{3} e^{4 x} sin (6 x) d x

= - \frac{1}{6} e^{4 x} cos (6 x) - (- \frac{2}{3} (\frac{1}{6} e^{4 x} sin (6 x) - \int \frac{2}{3} e^{4 x} sin (6 x) d x))

Take the constant out:

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

= - \frac{1}{6} e^{4 x} cos (6 x) - (- \frac{2}{3} (\frac{1}{6} e^{4 x} sin (6 x) - \frac{2}{3} \cdot \int e^{4 x} sin (6 x) d x))

Therefore

\int e^{4 x} sin (6 x) d x = - \frac{1}{6} e^{4 x} cos (6 x) - (- \frac{2}{3} (\frac{1}{6} e^{4 x} sin (6 x) - \frac{2}{3} \cdot \int e^{4 x} sin (6 x) d x))

Isolate

\int e^{4 x} sin (6 x) d x

= - \frac{3 e ^{4 x} cos ( 6 x )}{26} + \frac{e ^{4 x} sin ( 6 x )}{13}

Add a constant to the solution

= - \frac{3 e ^{4 x} cos ( 6 x )}{26} + \frac{e ^{4 x} sin ( 6 x )}{13} + C

\frac{1}{s ( s ( s + 4 ) + 3 )}

\frac{d}{d x} (11 x^{2} cot (x))

f (x) = 4

\int cos (v) sin (v) d v

\frac{\partial}{\partial x} (cos (6 y - x))

What is the integral of e^{4x}sin(6x) ?
The integral of e^{4x}sin(6x) is -(3e^{4x}cos(6x))/(26)+(e^{4x}sin(6x))/(13)+C