What is the integral of sinh(2t) ?

The integral of sinh(2t) is 1/2 cosh(2t)+C

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integral of sinh(2t)

\int sinh (2 t) d t

\frac{1}{2} cosh (2 t) + C

Solution steps

\int sinh (2 t) d t

Apply u-substitution

= \int sinh (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int sinh (u) d u

Use the common integral:

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

= \frac{1}{2} cosh (u)

Substitute back

u = 2 t

= \frac{1}{2} cosh (2 t)

Add a constant to the solution

= \frac{1}{2} cosh (2 t) + C