Question

Integrate...}- $\int\limits^2_1 {x^{-2} } \, dx$

Answer 1

Explanation:

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Integral ∫1−11x√1+x1−xln(2x2+2x+12x2−2x+1)dx

calculus integration definite-integrals contour-integration closed-form

I need help with this integral:I=∫1−11x√1+x1−xln(2x2+2x+12x2−2x+1) dx.

The integrand graph looks like this:

The approximate numeric value of the integral:I≈8.372211626601275661625747121...

Neither Mathematica nor Maple could find a closed form for this integral, and lookups of the approximate numeric value in WolframAlpha and ISC+ did not return plausible closed form candidates either. But I still hope there might be a closed form for it.

I am also interested in cases when only numerator or only denominator is present under the logarithm.