What Am I Doing Wrong with My Powers?

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what am i doing wrong here? its an easy problem but what the heck am i doing wrong?

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u5u1/2=u5+1/2=u11/2

Your powers are wrong for u
 


The problem is with the second term. u^5*u^(1/3) is not u^6.5.
 


Dustinsfl said:
u5u1/2=u5+1/2=u11/2

Your powers are wrong for u
11/2 = 5.5, so there's nothing wrong here.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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