What is the integral of 7e^{4x}cos(8x) ?

The integral of 7e^{4x}cos(8x) is 7((e^{4x}sin(8x))/(10)+(e^{4x}cos(8x))/(20))+C

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integral of 7e^{4x}cos(8x)

\int 7 e^{4 x} cos (8 x) d x

7 (\frac{e ^{4 x} sin ( 8 x )}{10} + \frac{e ^{4 x} cos ( 8 x )}{20}) + C

Solution steps

\int 7 e^{4 x} cos (8 x) d x

Take the constant out:

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

= 7 \cdot \int e^{4 x} cos (8 x) d x

Apply Integration By Parts

: \frac{1}{8} e^{4 x} sin (8 x) - \int \frac{1}{2} e^{4 x} sin (8 x) d x

= 7 (\frac{1}{8} e^{4 x} sin (8 x) - \int \frac{1}{2} e^{4 x} sin (8 x) d x)

Take the constant out:

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

= 7 (\frac{1}{8} e^{4 x} sin (8 x) - \frac{1}{2} \cdot \int e^{4 x} sin (8 x) d x)

Apply Integration By Parts

: - \frac{1}{8} e^{4 x} cos (8 x) - \int - \frac{1}{2} e^{4 x} cos (8 x) d x

= 7 (\frac{1}{8} e^{4 x} sin (8 x) - \frac{1}{2} (- \frac{1}{8} e^{4 x} cos (8 x) - \int - \frac{1}{2} e^{4 x} cos (8 x) d x))

Take the constant out:

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

= 7 (\frac{1}{8} e^{4 x} sin (8 x) - \frac{1}{2} (- \frac{1}{8} e^{4 x} cos (8 x) - (- \frac{1}{2} \cdot \int e^{4 x} cos (8 x) d x)))

Therefore

7 \cdot \int e^{4 x} cos (8 x) d x = 7 (\frac{1}{8} e^{4 x} sin (8 x) - \frac{1}{2} (- \frac{1}{8} e^{4 x} cos (8 x) - (- \frac{1}{2} \cdot \int e^{4 x} cos (8 x) d x)))

Isolate

\int e^{4 x} cos (8 x) d x

= 7 (\frac{e ^{4 x} sin ( 8 x )}{10} + \frac{e ^{4 x} cos ( 8 x )}{20})

Add a constant to the solution

= 7 (\frac{e ^{4 x} sin ( 8 x )}{10} + \frac{e ^{4 x} cos ( 8 x )}{20}) + C

f (x) = 2 x - 5

\int \frac{108}{w ^{2} 36 - w ^{2}} d w

\frac{d y}{d x} = 0.06 y - 24000

x \to \infty lim (5.3)

\frac{\partial}{\partial y} (yz e^{x z})

What is the integral of 7e^{4x}cos(8x) ?
The integral of 7e^{4x}cos(8x) is 7((e^{4x}sin(8x))/(10)+(e^{4x}cos(8x))/(20))+C