What is the integral of (cosh(4x)+sinh(2x)) ?

The integral of (cosh(4x)+sinh(2x)) is 1/4 sinh(4x)+1/2 cosh(2x)+C

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integral of (cosh(4x)+sinh(2x))

\int (cosh (4 x) + sinh (2 x)) d x

\frac{1}{4} sinh (4 x) + \frac{1}{2} cosh (2 x) + C

Solution steps

\int cosh (4 x) + sinh (2 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 cosh (4 x) d x + \int sinh (2 x) d x

\int cosh (4 x) d x = \frac{1}{4} sinh (4 x)

\int sinh (2 x) d x = \frac{1}{2} cosh (2 x)

= \frac{1}{4} sinh (4 x) + \frac{1}{2} cosh (2 x)

Add a constant to the solution

= \frac{1}{4} sinh (4 x) + \frac{1}{2} cosh (2 x) + C

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What is the integral of (cosh(4x)+sinh(2x)) ?
The integral of (cosh(4x)+sinh(2x)) is 1/4 sinh(4x)+1/2 cosh(2x)+C