Trigonometric Integral

• Oct 1st 2012, 06:31 PM
AlexCatran
Trigonometric Integral

The integral of arctan(x)arcsin(x)arcsinh(x)dx between -1 and 1.

Apologies for the formatting, I'll learn the tags as soon as possible =)
• Oct 1st 2012, 08:14 PM
TheEmptySet
Re: Trigonometric Integral
Quote:

Originally Posted by AlexCatran

The integral of arctan(x)arcsin(x)arcsinh(x)dx between -1 and 1.

Apologies for the formatting, I'll learn the tags as soon as possible =)

All three functions are odd. The product of three odd functions is odd. The integral of an odd function over a symetric interval is zero.

$\int_{-1}^{1}\tan^{-1}(x)\sin^{-1}(x)\sinh^{-1}(x)dx=0$
• Oct 1st 2012, 08:24 PM
AlexCatran
Re: Trigonometric Integral
That's fantastic, thank you.