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Thread: Integral Rule OR Trig Identity?

  1. #1
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    Integral Rule OR Trig Identity?

    What exactly is the following. I have never attempted to integrate something with a polynomial in the denominator.

    $\displaystyle \int\frac{1}{x^2+x+2}$
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  2. #2
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    Krizalid's Avatar
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    First off, don't even think about it, that polynomial is irreducible on $\displaystyle \mathbb R,$ so we may find another way of solving such integral.

    $\displaystyle \int{\frac{dx}{x^{2}+x+2}}=4\int{\frac{dx}{4x^{2}+ 4x+8}}=4\int{\frac{dx}{(2x+1)^{2}+7}}.$

    Now put $\displaystyle 2x+1=\sqrt7\tan\varphi.$
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