# many indefinite integrals do not evaluate in 10.1, looking for the cause

Bug introduced in 10.1 and fixed in 10.2

Many integrals no longer evaluate in V 10.1 when they did in 10.0.2

Here are some 23 integrals as an example, that all produced results in V 10.0.2, but now all returns unevaluated!

I am hoping there is some explanation to this which is common to all of them as many of them produced results (in 10.0.2) that involved Hypergeometric2F, but number of other integrals produced result which did not involve special functions.

That is why I think it is strange that so many no longer evaluate in 10.1, and so I think there is some one common issue they share, and hoping someone can shed some light on why these integrals do not evaluate any more.

I will list the integrals in source code first, then below that will put screen shot of results to compare in later edit.

Clear[d, e, x, f, m, p, c, n, A, B]
Integrate[Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]], x]
Integrate[1/Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]], x]

Integrate[
Sqrt[a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]]/(x*
Sqrt[-(a/b^2) + (a^2*x^2)/b^2]), x]

Integrate[
Sqrt[(-a)*x^2 + b*x*Sqrt[a/b^2 + (a^2*x^2)/b^2]]/(x*
Sqrt[a/b^2 + (a^2*x^2)/b^2]), x]

Integrate[
Sqrt[x*(a*x + b*Sqrt[-(a/b^2) + (a^2*x^2)/b^2])]/(x*
Sqrt[-(a/b^2) + (a^2*x^2)/b^2]), x]

Integrate[
Sqrt[x*(a*x + b*Sqrt[-(a/b^2) + (a^2*x^2)/b^2])]/(x*
Sqrt[-(a/b^2) + (a^2*x^2)/b^2]), x]

Integrate[
Sqrt[x*((-a)*x + b*Sqrt[a/b^2 + (a^2*x^2)/b^2])]/(x*
Sqrt[a/b^2 + (a^2*x^2)/b^2]), x]

Integrate[x^m Sqrt[b - a/x]/Sqrt[a - b x], x]
Integrate[(a + b Sqrt[c + d x])^p /x, x]
Integrate[x^(23/2)/Sqrt[a + b*x^5], x]
Integrate[x^(13/2)/Sqrt[a + b*x^5], x]
Integrate[x^(3/2)/Sqrt[a + b*x^5], x]
Integrate[x^(23/2)/Sqrt[1 + x^5], x]
Integrate[x^(13/2)/Sqrt[1 + x^5], x]
Integrate[x^(3/2)/Sqrt[1 + x^5], x]
Integrate[(x^4*(e + f*x)^n)/(a + b*x^2), x]
Integrate[(x^3*(e + f*x)^n)/(a + b*x^2), x]
Integrate[(x^2*(e + f*x)^n)/(a + b*x^2), x]
Integrate[(x*(e + f*x)^n)/(a + b*x^2), x]
Integrate[(e + f*x)^n/(a + b*x^2), x]
Integrate[(e + f*x)^n/(x*(a + b*x^2)), x]
Integrate[(e + f*x)^n/(x^2*(a + b*x^2)), x]
Integrate[(A + B*x)*((d + e*x)^m/(a + c*x^2)), x]
Integrate[x^m/(a + b*x^2 + c*x^4), x]


Again, all of the above fail to produce results in V 10.1, windows 7. But they all produce results in 10.0.2.

Will post screen shots below.

• Backslide? - interesting observation though! – dr.blochwave Apr 9 '15 at 8:28
• I suspect that this "regression" has to do with the presence of (complicated) branch points and branch cuts in the integrand, whose location depends on the value(s) of the parameter(s) in the integrand, and which have to be handled with extreme care if you want to get the correct result. Previously, Mathematica gave results that could be incorrect in such cases, so I presume Mathematica has been "regressed" whilst they work out a framework for handling such cases correctly. – Stephen Luttrell Apr 9 '15 at 10:37
• @StephenLuttrell But this does not seem to explain the ones with definite coefficients. – happy fish Apr 9 '15 at 14:34
• I have seen cases with definite coefficients for which Mathematica gives the right or wrong answer depending on where the integration limits are located. As far as I could tell, the errors occurred when Mathematica was being inconsistent with how it handled different branches of the integrand. – Stephen Luttrell Apr 9 '15 at 18:55
• Investigating as a regression. You can put a "bugs" tag on it if you like. – Daniel Lichtblau Apr 9 '15 at 20:48