What is the integral of sinh(4x) ?

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

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integral of sinh(4x)

\int sinh (4 x) d x

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

Solution steps

\int sinh (4 x) d x

Apply u-substitution

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

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

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

Add a constant to the solution

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

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