What is the integral of (9cos(x)+5sin(x)) ?

The integral of (9cos(x)+5sin(x)) is 9sin(x)-5cos(x)+C

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integral of (9cos(x)+5sin(x))

\int (9 cos (x) + 5 sin (x)) d x

9 sin (x) - 5 cos (x) + C

Solution steps

\int 9 cos (x) + 5 sin (x) d x

Apply the Sum Rule:

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

= \int 9 cos (x) d x + \int 5 sin (x) d x

\int 9 cos (x) d x = 9 sin (x)

\int 5 sin (x) d x = - 5 cos (x)

= 9 sin (x) - 5 cos (x)

Add a constant to the solution

= 9 sin (x) - 5 cos (x) + C

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What is the integral of (9cos(x)+5sin(x)) ?
The integral of (9cos(x)+5sin(x)) is 9sin(x)-5cos(x)+C