(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In each of the following cases use the given substitution in order to evaluate the given integral:

[tex]\int\frac{2+\sqrt x}{1-\sqrt x}dx=2(4(1+\sqrt x)^\frac{3}{2}-\frac{(1-\sqrt x)^2}{2}-3In(1-\sqrt x)[/tex]

2. Relevant equations

For the substitution

[tex]u=1-\sqrt x[/tex]

[tex]x=(1-u)^2[/tex]

3. The attempt at a solution

[tex]du=\frac{-1}{2\sqrt x}[/tex]

[tex]-2\sqrt x du=dx[/tex]

[tex]-2\sqrt(1-u)^2du=dx[/tex]

[tex]-2\int\frac{2+\sqrt(1-u)^2}{u}(\sqrt(1-u)^2[/tex]

[tex]-2\int 2\sqrt(1-u^2)(u^-1)du+ \sqrt(1-u^2)(u^-1)[/tex]

Guys how come when l simplify this integration l do not get the answer correct answer which is shown in the problem statement ? Where have l done my mistake ?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integration techniques

**Physics Forums | Science Articles, Homework Help, Discussion**