Two little integrals

Hello everybody. I'm stucked with two integrals.
I was trying to solve an integral by trigonometrical substitution:

1
Integral of: ------------
(36-x^2)^(4/2)

This is the integral of one over the square root of ((36 - x^2)^4)

Well... so I did all the trigonometric substitution and I get the
following integral:

1
--- Integral of: (secant of theta)^3 dtheta
216

My problem is that I cannot find an easy way to do the integral of (sec
x)^3. I've tryed every trigonometric property I know, integration by
parts, etc... and I get cyclic results that bring me nowhere.

Can someone tell me an easy method to solve this integral? My
calculator gets me a very long answer, like 6 additions so, is there
any way or are there any trigonometric properties to solve in an easier
way this integral? If not, how does the calculator gives so big
answers?

An the other one that I've tryed for days and I don't get even near to
the response (by the way I've tryed this one in 4 calculators and none
was able to do it) is:

Square root of: [sin(square root of x)] --> This one is not urgent, it
came outfor curiosity only, but the other one must be solvable, but,
how!?

Thank you!

.

Relevant Pages

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