What is the integral of sinh(3u) ?

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

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integral of sinh(3u)

\int sinh (3 u) d u

\frac{1}{3} cosh (3 u) + C

Solution steps

\int sinh (3 u) d u

Apply u-substitution

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int sinh (v) d v

Use the common integral:

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

= \frac{1}{3} cosh (v)

Substitute back

v = 3 u

= \frac{1}{3} cosh (3 u)

Add a constant to the solution

= \frac{1}{3} cosh (3 u) + C