How Do You Solve the Integral of (sec^2(sqrt(x)))/sqrt(x) Using u-Substitution?

mrdoe
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Find
\displaystyle\int\dfrac{\sec ^2\sqrt{x}}{\sqrt{x}} dx
We're supposed to use u du substitution but I can't seem to get this one.

EDIT: Sorry I didn't read rules.

I tried u=\sec^2\sqrt{x} and all variants. Usually it was in the form of

[sec or cos][^2 or none][sqrt x]
 
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Well a more intuitive substitution would be to take u=\sqrt{x}.
 
thanks, I can't see why I didn't see that
 
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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