I am very frustrated, mainly because my knowledge of Mathematica is abysmally low. I want to calculate the expected value of ln(x), where X is gamma(a,b) distributed, but it would seem that my Mathematica is bi-polar. I don't need the whole derivation, I only need the final expression.

I'm typing:

Integrate[

Log (theta)*(T^(d - m + 1)*theta^(d - m)*E^(-T*theta))/

Gamma[d - m + 1], {theta, 0, Infinity}]

but this gives a different answer than this

Integrate[

Log [theta]*(T^(d - m + 1)*theta^(d - m)*E^(-T*theta))/

Gamma[d - m + 1], {theta, 0, Infinity}]

thus using square brackets instead of round brackets in the log function in the beginning. The second one seems to be more correct since it contains a digamma function (which intuitively feels right) but the first one's expression is so much easier to work with.

Also, these two different expression that M gives are in no way similar.

Any help, or rather, should I use square brackets or round brackets?

Thanks !