What is the integral of (sinh(5x)+cosh(3x)) ?

The integral of (sinh(5x)+cosh(3x)) is 1/5 cosh(5x)+1/3 sinh(3x)+C

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integral of (sinh(5x)+cosh(3x))

\int (sinh (5 x) + cosh (3 x)) d x

\frac{1}{5} cosh (5 x) + \frac{1}{3} sinh (3 x) + C

Solution steps

\int sinh (5 x) + cosh (3 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 (5 x) d x + \int cosh (3 x) d x

\int sinh (5 x) d x = \frac{1}{5} cosh (5 x)

\int cosh (3 x) d x = \frac{1}{3} sinh (3 x)

= \frac{1}{5} cosh (5 x) + \frac{1}{3} sinh (3 x)

Add a constant to the solution

= \frac{1}{5} cosh (5 x) + \frac{1}{3} sinh (3 x) + C

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What is the integral of (sinh(5x)+cosh(3x)) ?
The integral of (sinh(5x)+cosh(3x)) is 1/5 cosh(5x)+1/3 sinh(3x)+C