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

By making the substituion [tex]t = \sqrt{1-x}[/tex]

find [tex]\int \frac{1}{2 + \sqrt{1 - x}}[/tex]

2. Relevant equations

3. The attempt at a solution

So [tex] t = (1-x)^\frac{1/2}[/tex]

[tex]t' = - \frac{1}{2} (1 - x)^{-\frac{1}{2}}[/tex]

[tex] dx = -2 \sqrt{1-x} dt [/tex]

[tex] \int \frac{-2 \sqrt{1-x}}{2 + \sqrt{1-x}} dt [/tex]

[tex] \int \frac{-2 \sqrt{1-x}}{2 + t} dt [/tex]

But am I anywhere useful? Am I allowed to say

[tex] \int \frac{-2t}{2 + t} dt [/tex]

because I've made the substation already? In that case it's a simple [tex] 2 ln|2+ \sqrt{1-x}|[/tex]

But that is wrong as the answer is a nasty:

[tex] 4ln|2+ \sqrt{1-x}| - 2 \sqrt{1-x} + c [/tex]

Thanks

Thomas

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# Homework Help: Substitution Question

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