Integrating 1 over root x times root x plus 1 - A Guide

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The integral of 1 over the quantity of root x times (root x plus 1) posed challenges for users, particularly with partial fractions and substitutions. A suggested substitution of x = u^2 was initially met with difficulty, leading to complications involving trigonometric functions. However, this substitution ultimately proved effective in simplifying the integral. The discussion highlights the importance of exploring different methods to solve complex integrals. The final resolution confirmed that the integral can be solved without involving quadratic terms or arctan functions.
Khan
Hey everyone, I just need a little help with this integral, I just can't get it:

integral of: (1/((x^(1/2)(x^(1/2)+1)) I know this is hard to read typed out, but said it is "Integral of 1 over the quantity root x times quantity root x plus 1. I tried doing partial fractions, but then I get stuck again.

Thanks in advance for your help!
 
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Did you try the substitution x = u2 to get rid of the roots?
 
I think I tried that, but that led me to a trig substition with arc tan and it's not leading my to the right answer, which I think is only with natural log.
 
Show me what you got; none of the terms involved should be quadratic, thus no arctan function.
 
Oh yea! The x=u^2 substitution did the trick actually, thanks for your help!
 

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