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This is not a question regarding a homework problem, but a step in class the professor did not show how to calculate.

**1. Homework Statement**

I am taking a course on Viscous Flow, and for Rayleigh flow after applying the similiarity solution : [tex]\eta=(y/(2*\sqrt{\gamma*t}))[/tex]

The x-momentum equation is given by [tex]f^{''}+2*\eta*f^{'}=0[/tex]

He states that "after integrating by parts the following solution is obtained"

[tex]f=C_{1}*\int(exp(-\eta^{2})*d\eta)+C_{2}[/tex] (integral is from 0 to [tex]\eta)[/tex]

I probably should, but I don't understand how to integrate the original governing equation by parts and obtain that solution. I have reviewed my old calculus books and cannot find any type of example which is similar. Can anyone shed any light?