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Math Help - integral

  1. #1
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    Question integral

    ∫ (1/X2 +4X+13) dX
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  2. #2
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    Quote Originally Posted by mindblowing View Post
    ∫ (1/X2 +4X+13) dX
    What do you mean?

    1)  \frac{1}{x^2+4x+13}

    2) \frac{1}{x^2} +4x +13 ?
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  3. #3
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    Quote Originally Posted by mindblowing View Post
    ∫ (1/X2 +4X+13) dX
    Are you familiar with the standard form \int \frac{a}{x^2 + a^2} \, dx = \tan^{-1} \left( \frac{x}{a}\right) + C ?

    Note that \frac{1}{x^2 + 4x + 13} = \frac{1}{(x + 2)^2 + 9} = \frac{1}{3} \, \left( \frac{3}{(x + 2)^2 + 3^2}\right).
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