Question

If\{d}{dx}f(x)=4x^{3}-\dfrac{3}{x^{4}} such that f(2)=0 then f(x) is

[tex]e^{2x+3}[\tex]

Answer 1

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.