What is the integral of sinh(8-9x) ?

The integral of sinh(8-9x) is -1/9 cosh(8-9x)+C

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integral of sinh(8-9x)

\int sinh (8 - 9 x) d x

- \frac{1}{9} cosh (8 - 9 x) + C

Solution steps

\int sinh (8 - 9 x) d x

Apply u-substitution

: \int - \frac{1}{9} sinh (u) d u

= \int - \frac{1}{9} sinh (u) d u

Take the constant out:

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

= - \frac{1}{9} \cdot \int sinh (u) d u

Use the common integral:

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

= - \frac{1}{9} cosh (u)

Substitute back

u = 8 - 9 x

= - \frac{1}{9} cosh (8 - 9 x)

Add a constant to the solution

= - \frac{1}{9} cosh (8 - 9 x) + C

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What is the integral of sinh(8-9x) ?
The integral of sinh(8-9x) is -1/9 cosh(8-9x)+C