### An integral to calculate

Posted:

**December 23 2015**I have a simple and native equation, but really struggle to find the way to it. Can anyone tell me how to calculate this integral

[tex]

\int^{x}_{0}\frac{y^{3/2} d y}{(1+y)^{3/2}}

[/tex]

I have trying various different ways to solve it, including changing variables from x to sinh function, cosh function etc., but failed. However, I tried it on mathematica and it indeed can find a solution:

[tex]

\frac{\sqrt{x}(x+3)}{(1+x)^{1/2}}-3 \ln ( \sqrt{1+x}+\sqrt{x} )

[/tex]

Please let me know if you have a smart way of doing the integral. this integral is crucial to solve the growth factor in the open universe model.

[tex]

\int^{x}_{0}\frac{y^{3/2} d y}{(1+y)^{3/2}}

[/tex]

I have trying various different ways to solve it, including changing variables from x to sinh function, cosh function etc., but failed. However, I tried it on mathematica and it indeed can find a solution:

[tex]

\frac{\sqrt{x}(x+3)}{(1+x)^{1/2}}-3 \ln ( \sqrt{1+x}+\sqrt{x} )

[/tex]

Please let me know if you have a smart way of doing the integral. this integral is crucial to solve the growth factor in the open universe model.