Improper Integral with Tricky Denominator: Solving (1+x)^-1/2

[annoymage]

Homework Statement

evaluate

$$\int$$ $$\frac{1}{(1+x)\sqrt{x}}$$ dx

Homework Equations

N/A

The Attempt at a Solution

how to do this, i can't use partial fraction, and integration by part makes it harder i guess, maybe using substitution, but how T_T
helpp

 

[Je m'appelle]

Hi, do you have the answer?

 

[annoymage]

no, why?

 

[Je m'appelle]

I tried to solve it through substitution, but I'm not sure if it's correct and would like to have it verified.

 

[annoymage]

can you tell me what substituion you are using please?

 

[Cyosis]

When you have an integral like this always try a few substitutions instead of just staring at it. Obvious substitutions would be u=1+x and u=sqrt(x). I will let you decide which one is the useful one.

 

[Je m'appelle]

I tried this:

$$u = \sqrt{x}$$

$$u^2 = x$$

Can you take over from here?

 

[annoymage]

thanks, i got the idea. thank you very much