NOTE ON A DEFINITE INTEGRAL. 125 



(1). 



COR. 1. Integrating by parts, we get 

 [log sin 0d0 = log sin - 

 The integrated part vanishes at both limits, 



COR. 2. Let sin 6 = e~& ; therefore the limits of x are 

 and oo, 



COR. 3. In this last integral, if we expand the denominator 



and as I e"" 1 * x dx = -j , we find 



111 1.311 1.3.5 



I . - 32 + ^ 5 ,+ j^-g 23 



