integral of dx/(1-x*sqrt(x))

Question

anonymous · Answer

$$\int\limits_{}^{} \frac{ dx }{ 1-x \sqrt{x} }$$

ganeshie8 · Answer

try $\sqrt{x} = u    $

ganeshie8 · Answer

$\implies  x = u^2  \implies dx = 2u~du$

ganeshie8 · Answer

$$\large \int \dfrac{2u~du}{1-u^3}$$

ganeshie8 · Answer

partial fractions etc..

anonymous · Answer

$$\int\limits_{}^{}\frac{ 1 }{ 1-u^2 } $$ equals to 
$$\frac{ 1 }{2  } \ln \frac{ 1+u }{ 1-u }$$
but what happends to $$\int\limits_{}^{}2u$$
because the answer in my books is
$$-\ln \frac{ \sqrt{x}-1 }{ \sqrt{x}+1 } +c$$

ganeshie8 · Answer

if possible, can you take a screenshot and attach..

anonymous · Answer

can't...writing from computer, and dont have cable for my phone to connect pics with.
but there is a page with identities of diffrent laws that states like this:
$$\frac{ 1 }{ a^2-x^2 }$$ where a^2 = 1^2 and x^2 = u^2
and that function has an indefinite integral of 
$$\frac{ 1 }{ 2a } \ln \frac{ a+x }{ a-x } +c$$
a =1 and x = sqrt(x)

ganeshie8 · Answer

that identity looks correct, but it may not be useful for our present problem

ganeshie8 · Answer

wolfram gives this : http://www.wolframalpha.com/input/?i=%5Cint+1%2F%281-xsqrt%28x%29%29+dx

anonymous · Answer

thanx