What is the integral of (8cos(8w)-7sin(7w)) ?

The integral of (8cos(8w)-7sin(7w)) is sin(8w)+cos(7w)+C

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integral of (8cos(8w)-7sin(7w))

\int (8 cos (8 w) - 7 sin (7 w)) d w

sin (8 w) + cos (7 w) + C

Solution steps

\int 8 cos (8 w) - 7 sin (7 w) d w

Apply the Sum Rule:

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

= \int 8 cos (8 w) d w - \int 7 sin (7 w) d w

\int 8 cos (8 w) d w = sin (8 w)

\int 7 sin (7 w) d w = - cos (7 w)

= sin (8 w) - (- cos (7 w))

Simplify

= sin (8 w) + cos (7 w)

Add a constant to the solution

= sin (8 w) + cos (7 w) + C

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What is the integral of (8cos(8w)-7sin(7w)) ?
The integral of (8cos(8w)-7sin(7w)) is sin(8w)+cos(7w)+C