# Evaluate the integral

• May 2nd 2009, 02:05 AM
simplependulum
Evaluate the integral
• May 2nd 2009, 06:12 AM
running-gag
Hi

Spoiler:

$\int \frac{dx}{x(1+x^{2009})} = \int \left(\frac{1}{x}-\frac{x^{2008}}{1+x^{2009}}\right) \: dx = \ln x - \frac{\ln(1+x^{2009})}{2009}$
• May 2nd 2009, 06:21 AM
NonCommAlg
Quote:

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 $\int \frac {dx}{x(1 + x^{\alpha})} = - \int \frac {t^{\alpha - 1}}{1+t^{\alpha}} \ dt = - \frac{1}{\alpha} \ln |1 + t^{\alpha}| + c=-\frac{1}{\alpha} \ln |1 + x^{-\alpha}| + c.$
• May 2nd 2009, 07:39 PM
simplependulum
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 (Crying) I had no confidence to solve at that time