Math Is Fun Forum

hypsin_0

Member

From: Earth

Registered: 2025-07-05

Posts: 148

Website

an integral question

---

This is not a signature.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,828

Re: an integral question

I'm a bit rusty on these but I think you can use the substitution

tan u = nx^(n-1).  This produces an integral in (sec u)^3 which can be 'done' by integration by parts.

I'll see if I can do the whole thing but, by all means, beat me to it, I'm off to the dentist now

LATER EDIT: I was getting 'well tied up' in the algebra so I thought I'd better ask my 'pal' google ai.  Not good news I'm afraid. Here's what it said:

The integral does not have a general closed-form expression in terms of elementary functions for all n. However, it can be expressed using the Gaussian hypergeometric function
or evaluated for specific values of n.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob