Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have tried to find $$\int{\biggl(\dfrac{\sqrt{x+1}}{x-1}\biggr)^x}dx$$ but I don't know how to do it, because it combines $u^x$ and $\dfrac{u}{v}$.

share|cite|improve this question
You are sure this has an elementary antiderivative? Where is this function from? – martini Apr 27 '12 at 6:59
Wolfram Alpha can't find an elementary antiderivative (and neither can I!) – user29743 Apr 27 '12 at 7:01
This looks evil! – Tomarinator Apr 27 '12 at 7:23
@martini No. That's why I've asked. The function comes from my imagination… – Garmen1778 Apr 27 '12 at 16:29
@Garmen1778 The problem with our imagination is that it can create problems which noone can solve ;) – N. S. May 3 '12 at 20:00
up vote 1 down vote accepted

You can do... $$\int f(x)^x\; dx=\int e^{x\ln f(x)}\; dx=\int e^{\alpha(x)}\; dx$$ where $f(x)=\frac{\sqrt{x+1}}{x-1}$

share|cite|improve this answer
-1 Yes, you can, but does it lead you anywhere? – Sasha May 8 '12 at 14:46
Mmm... It was a simple idea. (¬¬) – diofanto May 8 '12 at 15:17
that logarithm isn't a neperian logarithm, expressed with $\ln f(x)$? – Garmen1778 May 8 '12 at 21:09
@Garmen1778 I have tried googling "neperian logarithms" couldn't find that term. Could you tell me what it is? – yiyi May 9 '12 at 2:45
Ups, sorry, I mean natural logarithm, expressed by $\ln f(x)$ or $\log_e f(x)$ – Garmen1778 May 9 '12 at 5:37

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.