Effective Methods for Solving \int\frac{x^{2} - 1}{x} | Get Help Now!

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1. How would I do this: \int\frac{x^{2} - 1}{x}

I don't need the answer, only the method I need to use (integration by parts, partial fractions etc.)

Thanks.
 
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Just observe that

\frac{x^2-1}{x}=\frac{x^2}{x}-\frac{1}{x}
 
ahh now i feel dumb. Thanks man.
 
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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