# Mathematica 9 cannot solve this Integral. Mathematica 8 could. Is this a bug?

I was trying to (re)calculate a problem of an older Wolfram blog post (Problem 11457, by M. L. Glasser) with Mathematica 9.0.0.0 (on OS X 10.8.2).

Assuming[0 < a < b, Integrate[ArcCos[x/Sqrt[(a + b) x - a b]], {x, a, b}]]


Instead of the expected solution, it just returns the integral unevaluated. Is this a regression?

More details: As pointed out in the commentes, the indefinite integral

Integrate[ArcCos[x/Sqrt[(a + b) x - a b]], x]


still gives the same result in Mathematica 8 and 9.

The next two each returned ConditionalExpression in Mathematica 8 but return unevaluated in Mathematica 9:

Integrate[ArcCos[x/Sqrt[(a + b) x - a b]], {x, a, b}]
Integrate[ArcCos[x/Sqrt[(a + b) x - a b]], {x, a, b}, Assumptions -> 0 <= a <= b]


The actual problem

Integrate[ArcCos[x/Sqrt[(a + b) x - a b]], {x, a, b}, Assumptions -> 0 < a < b]


computes correctly to ((a - b)^2 \[Pi])/(4 (a + b)) in Mathematica 8 but still returns unevaulated in Mathematica 9.

• I can confirm that it does not work in MMA 9 win 7 64 bit, but works in MMA 8.0.1. In MMA8 I get ((a - b)^2 \[Pi])/(4 (a + b)) Jan 24, 2013 at 12:16
• The topic is misleading. I thought it was about Regression in Statistics
– asim
Jan 24, 2013 at 14:35
• Mathematica 8 and 9 give the same correct indefinite integral. The difference is in the calculation for the limits of integration. Jan 24, 2013 at 15:45
• Here are another instances of definite integrals which are unevaluated in ver.9 while they are in ver.8 mathematica.stackexchange.com/questions/18327/… Jan 24, 2013 at 17:18
• [I am NOT putting this into a response.] Yes, this appears to be a regression. Investigating... Jan 25, 2013 at 1:18

Assuming[0 < a < b,