What is the integral of zsin(z)-cos(z) ?

The integral of zsin(z)-cos(z) is -zcos(z)+C

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integral of zsin(z)-cos(z)

\int z sin (z) - cos (z) d z

- z cos (z) + C

Solution steps

\int z sin (z) - cos (z) d z

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int z sin (z) d z - \int cos (z) d z

\int z sin (z) d z = - z cos (z) + sin (z)

\int cos (z) d z = sin (z)

= - z cos (z) + sin (z) - sin (z)

Simplify

= - z cos (z)

Add a constant to the solution

= - z cos (z) + C

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What is the integral of zsin(z)-cos(z) ?
The integral of zsin(z)-cos(z) is -zcos(z)+C