For the following two integrals,

1. $\displaystyle \int_0^1 \frac{1}{1-x^b} dx$

2. $\displaystyle \int_0^1 \frac{x^{ab}}{1-x^b} dx$

is there any closed forms in terms of (Star)trigonometric functions(Star) ???

thanks for helping

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- Jan 22nd 2008, 11:01 PMgraticcioIntegration - looking for closed form
For the following two integrals,

1. $\displaystyle \int_0^1 \frac{1}{1-x^b} dx$

2. $\displaystyle \int_0^1 \frac{x^{ab}}{1-x^b} dx$

is there any closed forms in terms of (Star)trigonometric functions(Star) ???

thanks for helping - Jan 22nd 2008, 11:16 PMmr fantastic
- Jan 22nd 2008, 11:24 PMgraticcio
yes, but there appears to be a pattern...

some arctan and some log...

can we use any trigonometric substitution to evaluate?

thanks - Jan 23rd 2008, 12:00 AMmr fantastic
- Jan 23rd 2008, 01:20 AMgraticcio
so what is the relationship between hypergeometric function and trigonometric function in this case ???

or how to represent the hypergeometric function here by trigonometric functions?

thanks - Jan 23rd 2008, 01:27 AMwingless
- Jan 23rd 2008, 01:48 AMgraticcio
they converge with x<1

- Jan 23rd 2008, 02:08 AMwingless