Recommended AP calculus assistance material?

dnt
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sorry if this doesn't belong here - please feel free to move it to the proper section.

im looking for a good book/reference material that would be helpful during a year of HS AP calculus. something that will supplement the school material and help me better understand it as we go through it.

any recommendations?
 
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An AP Review book by Barron's or Princeton Review would be useful. The Barron's is "harder" than the test, and has good practice problems.
 
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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