finding the integral possbily u sub?

**genlovesmusic09** · December 5th 2009, 12:47 PM

$\int_0^1 {\frac{{{x^{\frac{1} {2}}}}} {{{{(1 - x)}^{\frac{1} {2}}}}}dx} $

I am thinking u substitution but I am not sure what to sub in

**mr fantastic** · December 5th 2009, 12:51 PM

Originally Posted by genlovesmusic09

$\int_0^1 {\frac{{{x^{\frac{1} {2}}}}} {{{{(1 - x)}^{\frac{1} {2}}}}}dx} $

I am thinking u substitution but I am not sure what to sub in

See here: - Wolfram|Alpha

Be sure to click on Show steps.

**genlovesmusic09** · December 6th 2009, 05:23 PM

can't you do a trig sub with arc sin because the bottom is (1-x)^.5

**HallsofIvy** · December 6th 2009, 06:19 PM

Originally Posted by genlovesmusic09

can't you do a trig sub with arc sin because the bottom is (1-x)^.5

But the derivative of arcsin is $\frac{1}{(1- x^2)^{.5}}$ , not $\frac{1}{(1-x)^{.5}}$ .

**genlovesmusic09** · December 6th 2009, 06:40 PM

Originally Posted by HallsofIvy

But the derivative of arcsin is $\frac{1}{(1- x^2)^{.5}}$ , not $\frac{1}{(1-x)^{.5}}$ .

but if i do a u sub where u=x^.5 then x=u^2
so it would be u/(1-u^2)^.5

**mr fantastic** · December 6th 2009, 06:49 PM

Originally Posted by genlovesmusic09

but if i do a u sub where u=x^.5 then x=u^2
so it would be u/(1-u^2)^.5

No it doesn't. Have you considered what dx becomes ....?

Thread: finding the integral possbily u sub?