Mastering Calculus: Tips, Tutorials, and Resources for Success

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Petradog
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I know Pre-Calculus

I need to learn Calculus, Matrices, and Set Theory

How can I learn Calculus and what websites have good tutorials?
 
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The best way to learn calculus is just to buy a book and go through it (don't just read it, do lots of exercises). If you have a solid understanding of high school math, then this shouldn't pose a problem. If it does then you should go back to the basics. I don't think that a tutorial is necessary. The best textbook to use depends on what you need the calculus for.
 
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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