What is the integral of zsin(8z) ?

The integral of zsin(8z) is -1/8 zcos(8z)+1/64 sin(8z)+C

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integral of zsin(8z)

\int z sin (8 z) d z

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

Solution steps

\int z sin (8 z) d z

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (x e^{x} cos (y))

\frac{d}{d x} (arcsin (5 x + 1))

n = 0 \sum \infty \frac{e n}{3 n + 1}

\frac{6}{x}

t e^{- t^{5}}

What is the integral of zsin(8z) ?
The integral of zsin(8z) is -1/8 zcos(8z)+1/64 sin(8z)+C