Help with Indefinite integrals.

master1425
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Homework Statement


\int sinx/(1+cos^{2}x)dx


Can anyone help me with this problem?
 
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Did you try substituting u=cos(x) as a first step??
 
Ah ok, that was my biggest problem. I tried substituting u=1+cos^2x and u=sinx. But neither yielded the result I wanted.

So I will try using just u=cosx and see how that works for me.
 
Ok, I got that one finally.

How about this one?

\int x^{2}sinx/1+x^{6} dx

I tried u=sinx, but got stuck. Is that what I need to use? Any help would be appreciated.
 
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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