What is the integral of (8sin(x)+9sinh(x)) ?

The integral of (8sin(x)+9sinh(x)) is -8cos(x)+9cosh(x)+C

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integral of (8sin(x)+9sinh(x))

\int (8 sin (x) + 9 sinh (x)) d x

- 8 cos (x) + 9 cosh (x) + C

Solution steps

\int 8 sin (x) + 9 sinh (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 8 sin (x) d x + \int 9 sinh (x) d x

\int 8 sin (x) d x = - 8 cos (x)

\int 9 sinh (x) d x = 9 cosh (x)

= - 8 cos (x) + 9 cosh (x)

Add a constant to the solution

= - 8 cos (x) + 9 cosh (x) + C

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What is the integral of (8sin(x)+9sinh(x)) ?
The integral of (8sin(x)+9sinh(x)) is -8cos(x)+9cosh(x)+C