What is the integral of 2zsin(2z)-cos(2z) ?

The integral of 2zsin(2z)-cos(2z) is -zcos(2z)+C

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integral of 2zsin(2z)-cos(2z)

\int 2 z sin (2 z) - cos (2 z) d z

- z cos (2 z) + C

Solution steps

\int 2 z sin (2 z) - cos (2 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 2 z sin (2 z) d z - \int cos (2 z) d z

\int 2 z sin (2 z) d z = - z cos (2 z) + \frac{1}{2} sin (2 z)

\int cos (2 z) d z = \frac{1}{2} sin (2 z)

= - z cos (2 z) + \frac{1}{2} sin (2 z) - \frac{1}{2} sin (2 z)

Add similar elements:

\frac{1}{2} sin (2 z) - \frac{1}{2} sin (2 z) = 0

= - z cos (2 z)

Add a constant to the solution

= - z cos (2 z) + C

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What is the integral of 2zsin(2z)-cos(2z) ?
The integral of 2zsin(2z)-cos(2z) is -zcos(2z)+C