Does anyone know how to integrate this expression for x please?:

ln(ax^n + c)

a, n and c are of course constants, and bot a and c should be positive but n will tend to be negative.

https://www.wolframalpha.com/input/?i=integrate+ln(a*x%5En+%2B+c)+for+x

I've no idea if the solution is correct but it's certainly far more likely to be than what I would come up with!

This might be the correct method, I'm no expert at getting Woflram to do what I want.

https://www.wolframalpha.com/input/?i=integrate+ln(a*x%5En+%2B+c)*dx

Does anyone know how to integrate this expression for x please?:

ln(ax^n + c)

a, n and c are of course constants, and bot a and c should be positive but n will tend to be negative.

Why are you trying to do that? Without context it's hard to know if using a numerical method would be acceptable, for instance.

I don't suppose these links will provide proofs will they? Jesus, I didn't realize it would involve the hypergeometric function!

I don't suppose these links will provide proofs will they? Jesus, I didn't realize it would involve the hypergeometric function!

It might not, I'm not an expert at putting things in Wolfram so the links may be incorrect. It can show the steps but I think you need a paid account for that.