Evaluate the integral

**simplependulum** · May 2nd 2009, 02:05 AM

Evaluate the integral :

**running-gag** · May 2nd 2009, 06:12 AM

Hi

Spoiler:

**NonCommAlg** · May 2nd 2009, 06:21 AM

Originally Posted by simplependulum

Evaluate the integral : $\int \frac{dx}{x(1 + x^{2009})}.$

let $\alpha > 0$ and put $x = \frac{1}{t}.$ then we get $\int \frac {dx}{x(1 + x^{\alpha})} = - \int \frac {t^{\alpha - 1}}{1+t^{\alpha}} \ dt = - \frac{1}{\alpha} \ln |1 + t^{\alpha}| + c=-\frac{1}{\alpha} \ln |1 + x^{-\alpha}| + c.$

**simplependulum** · May 2nd 2009, 07:39 PM

Yes . It isn't difficult actually

but I was shocked and scared when my friend gave me this integral because the degree is too large 2009

I had no confidence to solve at that time

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