- #1

Gondur

- 25

- 0

## Homework Statement

Find the anti derivative of [tex] \int xcosh (x^2) dx[/tex]

## Homework Equations

By parts formula and Hyperbolic Identities of sinh x and cosh x as well as others

## The Attempt at a Solution

[tex] \int xcosh (x^2) dx[/tex]

The problem I'm having is integrating [tex] \int cosh (x^2) dx[/tex]

I tried setting variables [tex]u=x[/tex] and [tex]\frac{dv}{dx}= \int cosh (x^2) dx[/tex] with the assumption this could be solved using the by parts formula.

I then concentrated specifically on solving [tex] \int cosh (x^2) dx[/tex]. I haven't found a method that I know of that's appropriate given that the composite is (x^2) and not (cosh x)^2. Wolfram Alpha shows the solution with an error function - which I know nothing about yet.

I've touched up on Euler's formula [tex]cosx+isinx=e^{ix}[/tex] and its parallel [tex]sinhx+coshx=e^x[/tex] and I'm just about to learn its applications, maybe it should be used here. This area is new to me so light explanations are wise at this time.