What is the integral of (4sin(x)+5sinh(x)) ?

The integral of (4sin(x)+5sinh(x)) is -4cos(x)+5cosh(x)+C

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integral of (4sin(x)+5sinh(x))

\int (4 sin (x) + 5 sinh (x)) d x

- 4 cos (x) + 5 cosh (x) + C

Solution steps

\int 4 sin (x) + 5 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 4 sin (x) d x + \int 5 sinh (x) d x

\int 4 sin (x) d x = - 4 cos (x)

\int 5 sinh (x) d x = 5 cosh (x)

= - 4 cos (x) + 5 cosh (x)

Add a constant to the solution

= - 4 cos (x) + 5 cosh (x) + C

What is the integral of (4sin(x)+5sinh(x)) ?
The integral of (4sin(x)+5sinh(x)) is -4cos(x)+5cosh(x)+C