What is the integral of sinh(3-4x) ?

The integral of sinh(3-4x) is -1/4 cosh(3-4x)+C

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integral of sinh(3-4x)

\int sinh (3 - 4 x) d x

- \frac{1}{4} cosh (3 - 4 x) + C

Solution steps

\int sinh (3 - 4 x) d x

Apply u-substitution

= \int - \frac{1}{4} sinh (u) d u

Take the constant out:

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

= - \frac{1}{4} \cdot \int sinh (u) d u

Use the common integral:

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

= - \frac{1}{4} cosh (u)

Substitute back

u = 3 - 4 x

= - \frac{1}{4} cosh (3 - 4 x)

Add a constant to the solution

= - \frac{1}{4} cosh (3 - 4 x) + C

What is the integral of sinh(3-4x) ?
The integral of sinh(3-4x) is -1/4 cosh(3-4x)+C