Hyperbolic Integraton problem

Question

Solve step by step.

Answer 1

The Function is .

Multiply and divide the expression by cosh(x).

We know that cosh²(x) - sinh²(x) = 1 ⇒ cosh²(x) = 1 + sinh²(x)

Let us consider u = sinh(x)

Apply derivative with respect to x.

du = cosh(x) dx

We know that .

Substitute u = sinh(x)

Therefore .