- #1
noblerare
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[SOLVED] Several Integrals
[tex]\int[/tex][tex]\frac{xdx}{\sqrt{1-x}}[/tex]
n/a
I tried to multiple top and bottom by the conjugate:
[tex]\int[/tex][tex]\frac{x\sqrt{1+x}dx}{\sqrt{1-x^{2}}}[/tex]
After trig substitution, I end up with:
-[tex]\int[/tex]cos[tex]\theta[/tex][tex]\sqrt{1+cos\theta}[/tex]d[tex]\theta[/tex]
I've also tried u-substitution but nothing seems to work.
Can anyone help me out on this? And show steps, please? Thanks so much!
Homework Statement
[tex]\int[/tex][tex]\frac{xdx}{\sqrt{1-x}}[/tex]
Homework Equations
n/a
The Attempt at a Solution
I tried to multiple top and bottom by the conjugate:
[tex]\int[/tex][tex]\frac{x\sqrt{1+x}dx}{\sqrt{1-x^{2}}}[/tex]
After trig substitution, I end up with:
-[tex]\int[/tex]cos[tex]\theta[/tex][tex]\sqrt{1+cos\theta}[/tex]d[tex]\theta[/tex]
I've also tried u-substitution but nothing seems to work.
Can anyone help me out on this? And show steps, please? Thanks so much!