What is the integral of-sinh(18x) ?

The integral of-sinh(18x) is -1/18 cosh(18x)+C

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integral of-sinh(18x)

\int - sinh (18 x) d x

- \frac{1}{18} cosh (18 x) + C

Solution steps

\int - sinh (18 x) d x

Take the constant out:

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

= - \int sinh (18 x) d x

Apply u-substitution

: \int sinh (u) \frac{1}{18} d u

= - \int sinh (u) \frac{1}{18} d u

Take the constant out:

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

= - \frac{1}{18} \cdot \int sinh (u) d u

Use the common integral:

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

= - \frac{1}{18} cosh (u)

Substitute back

u = 18 x

= - \frac{1}{18} cosh (18 x)

Add a constant to the solution

= - \frac{1}{18} cosh (18 x) + C

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What is the integral of-sinh(18x) ?
The integral of-sinh(18x) is -1/18 cosh(18x)+C