Help Me Integrate sin2(x): Tips & Tricks

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Homework Statement


For whatever reason, I'm having issues integrating sin2(x)


Homework Equations


I can use U-sub, trig-sub, integration by parts, partial fractions, in any combination as needed


The Attempt at a Solution


My brain is failing me, so any hints would be awesome.
 
Last edited:
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Use a double angle formula for the last one. cos(2x)=?
 
i have that in my table of integrals in the back of my calc book. That's where i'd look. heh
 
sweet it worked :D
thanks a bunch
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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