or 



INVERSE METHOD OF DEFINITE INTEGRALS. 339 



hence 



^-/ 1 I 



+ 1 I 



_ \«-a)(/3-a)| ^ 1 r 1 W + 



, (n + mn + 2) 1 L_ + &cl 



(« + !)(« + 2) 



Commuting in this equation the quantities a and /3, we have 



(» + !)(» + 2) 1 1 



,., '^"{(f-/3)(a-/3)} _ 1 r . ^ ^ + 11 1 



(» + l)U + 2) 1 1 1 



1.2 ■ {a-(iy{t^(iy^ ^^■j 



If both equations be added observing that 



1 1 



+ 



(#-a)(/3-a) ^ (/-/3)(«-/3) {t-a){^-t)' 



the sum of the left-hand members 



fpn £ 



1^2'.3^...M'«?a"C?/3" 



rf".-^ ef-. ^ 



^_1)„^ ^-« /3-^ 



1.2.3...wrfa"' 1 .2.3...W6?/3" 

 1 1 



Vol. V. Part III. Yy 



