A Refresher from Calc I to DiffEQ?

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TheNE
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I need some help, guys. I've taken Calc I -> DiffEQ, but I don't remember everything well. My NukeE courses are growing increasingly difficult (using calculus/diffeq that I forgot how to use). What would you guys recommend doing as a refresher to pick it all back up?! Thank you!
 
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if you're going for analytical, rudimentary solutions google "pauls notes" and go from there. he covers everything from single variable to vector calculus, ordinary differential equation and partial diffeq!

he provides some theory but nothing too rigorous (and from what it sounds like you don't want that route anyway).

good luck!
 
Thank you, joshmccraney. I have examined pauls notes before. They are pretty helpful too! Sometimes discerning the material can be tough though.
 
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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