# Serious regression in Integrate in 11.1.1? Division by zero generated

seen first in 11.1.1, Fixed in 11.2

What is going on here? In version 11.1.1 on windows 7

Using Version 11.0.1 also on windows 7

Source code

ClearAll[x, n, c, a ,b]
Integrate[(a + b*(c*x^n)^(2/n))^3, x]


Why does Mathematica give 1/0 now in the latest update? Do you think this is a new bug?

• If you want, you can try traceView2[ Trace[Integrate[(a + b*(c*x^n)^(2/n))^3, x], TraceInternal -> True]] to find out where things go wrong. – QuantumDot Jul 1 '17 at 20:49
• Slightly more minimal example triggering the bug: Integrate[(1 + (x^n)^(-n^(-1)))^2, x] – QuantumDot Jul 1 '17 at 21:02
• @QuantumDot Yes, I found many more little simpler examples. This one also triggers it: Integrate[(a+(c*x^n)^(2/n))^3,x] but changing to Integrate[(a+(c*x^n)^(1/n))^3,x] and error goes away! I just copied the one from the file I was running and posted that. I get more integrals now with same error. But I am sure they are all due to same bug. – Nasser Jul 1 '17 at 21:07

## 2 Answers

Obviously, this is a bug. It actually dates to 11.1.0. I checked with the relevant developer. We have a fix in our internal development build, and we'll try to get it into the next release.

This is one of those funny cases where a bugfix elsewhere caused a slightly different path to be traversed inside Integrate, and that path was missing a check for division by zero.

fyi; This bug is now fixed in 11.2. Thank you WRI