What is the integral of sinh(x)+cosh(x) ?

The integral of sinh(x)+cosh(x) is cosh(x)+sinh(x)+C

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integral of sinh(x)+cosh(x)

\int sinh (x) + cosh (x) d x

cosh (x) + sinh (x) + C

Solution steps

\int sinh (x) + cosh (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 sinh (x) d x + \int cosh (x) d x

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

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

= cosh (x) + sinh (x)

Add a constant to the solution

= cosh (x) + sinh (x) + C

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What is the integral of sinh(x)+cosh(x) ?
The integral of sinh(x)+cosh(x) is cosh(x)+sinh(x)+C