Separate the integrals, and then use integration by parts.
I think this is not correct. If we try to differentiate the right hand side, we don't get the function . For example, there is no closed form for .
To answer the question, note that . Now, change your variable and continue (you may need to integrate by parts)
But it gets very messy!
http://www.wolframalpha.com/input/?i=integrate+e^(0.5*x^2-1.5*ln(x)%2Bc)dx++
The answer is not encouraging :S
Well the only mysterious symbol is which is known as the Gamma function. It can be explained as a generalization of the factorial operator. It works on all real numbers. It is defined as integral.
check it: Gamma Function -- from Wolfram MathWorld