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I've been trying to integrate this:

$\int_0^\infty \frac{1}{x^2 + 2x + 2} \mathrm{d} x .$

Unfortunately I haven't found a way so far. I've been trying to factor the denominator in order to end up with partial fractions. Is there a way to factor it? If so, I can't remember any, so if you could remind me how to do it, it would be nice.

Thanks for your help.

2 Answers 2

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Try using the equation: $x^2+2x+2=(x+1)^2+1$

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    If trying to use partial fractions, the first thing I would do is check the discriminant $b^2 - 4ac$. This will immediately tell you if it's irreducible or not, and if it is you can use the quadratic formula to find the zeroes, and hence the factorization into linear factors.2012-03-20
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$ \int\limits_0^\infty \frac{dx}{x^2+2x+2}= \lim\limits_{t\to\infty}\int\limits_0^t\frac{dx}{x^2+2x+2}= \lim\limits_{t\to\infty} \arctan(x+1)|_0^t= $ $ \lim\limits_{t\to\infty} \arctan(t+1)-\arctan(1)=\frac{\pi}{2}-\frac{\pi}{4}=\frac{\pi}{4} $

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    do it like this `$\int \mathrm{d}x$` (becomes $\int \mathrm{d}x$) and right click on equations to see how the source.2011-12-26