While attempting to integrate ln(x+1)

I got it down to xln(x+1) - the integral of x/(x+1)

If integration by parts is done again the problem repeats itself.

My teacher tells me the answer is xln(x+1) - x + ln(x+1) + c

How did he get there?

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- Sep 24th 2009, 07:50 AMPD1337Help with Integration by Parts Problem
While attempting to integrate ln(x+1)

I got it down to xln(x+1) - the integral of x/(x+1)

If integration by parts is done again the problem repeats itself.

My teacher tells me the answer is xln(x+1) - x + ln(x+1) + c

How did he get there? - Sep 24th 2009, 08:00 AMred_dog
$\displaystyle \int\frac{x}{x+1}dx=\int\frac{x+1-1}{x+1}dx=\int\left(1-\frac{1}{x+1}\right)dx$

Continue now. - Sep 24th 2009, 08:02 AMPD1337
Got it! Thanks for your help