What is the integral of xsin(8x) ?

The integral of xsin(8x) is -1/8 xcos(8x)+1/64 sin(8x)+C

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integral of xsin(8x)

\int x sin (8 x) d x

- \frac{1}{8} x cos (8 x) + \frac{1}{64} sin (8 x) + C

Solution steps

\int x sin (8 x) d x

Apply Integration By Parts

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

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

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

= - \frac{1}{8} x cos (8 x) - (- \frac{1}{64} sin (8 x))

Simplify

= - \frac{1}{8} x cos (8 x) + \frac{1}{64} sin (8 x)

Add a constant to the solution

= - \frac{1}{8} x cos (8 x) + \frac{1}{64} sin (8 x) + C

n = 1 \sum \infty 4 (- \frac{1}{7})^{4 n}

\int x sin (9 - x) d x

\frac{d}{d x} (2 arctan (\frac{1}{x}))

7 t

\frac{d}{d x} (cot (π x))

What is the integral of xsin(8x) ?
The integral of xsin(8x) is -1/8 xcos(8x)+1/64 sin(8x)+C