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Home Q & A Board Science-Related Homework Help Mathematics
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SmithNL SmithNL
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11 years ago
The problem is: the integral of dx / x^2 + x + 1

I have to complete the square on the quadratic and make a substitution and then evaluate. How do I go about doing this without changing the value of the integrand??

Much thanks Slight Smile
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#1
11 years ago
Change the integral to that of dx/(Y^2 + A), where Y = X + 1/2, and you can calculate the constant A.

But that's the same as the integral of dY/(Y^2 + A).

Hopefully you can solve that directly.

If not, let B be a constant such that Z = - B^2, and look at the relationship between 1/(Y^2 - B^2) and [1/(Y-B) - 1/(Y+B)].  (One's a constant multiple of the other.)

You should be able to fill in the blanks.
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