What is the integral of sinh(5x) ?

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

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integral of sinh(5x)

\int sinh (5 x) d x

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

Solution steps

\int sinh (5 x) d x

Apply u-substitution

: \int sinh (u) \frac{1}{5} d u

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

Take the constant out:

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

= \frac{1}{5} \cdot \int sinh (u) d u

Use the common integral:

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

= \frac{1}{5} cosh (u)

Substitute back

u = 5 x

= \frac{1}{5} cosh (5 x)

Add a constant to the solution

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

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