What is the integral of cosh^2(v) ?

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

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integral of cosh^2(v)

\int cosh^{2} (v) d v

\frac{1}{2} (v + \frac{1}{2} sinh (2 v)) + C

Solution steps

\int cosh^{2} (v) d v

Rewrite using trig identities

= \int \frac{1 + cosh ( 2 v )}{2} d v

Take the constant out:

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

= \frac{1}{2} \cdot \int 1 + cosh (2 v) d v

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int 1 d v + \int cosh (2 v) d v)

\int 1 d v = v

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

= \frac{1}{2} (v + \frac{1}{2} sinh (2 v))

Add a constant to the solution

= \frac{1}{2} (v + \frac{1}{2} sinh (2 v)) + C

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What is the integral of cosh^2(v) ?
The integral of cosh^2(v) is 1/2 (v+1/2 sinh(2v))+C