INTEGRATION BY PARTS 185 



To integrate a^e 8 * 

 (x*t?* dx - la^e 3 * - | I 



8 8 



To integrate ^"(logg x) m , put log e a? = y 

 Then = e v and da: = e w dy 



I a;* 1 (log^)" 1 <ir = \e nv y m e v dy 



= ft/" e( n+1 ) dy 



The integral thus reducing down to a form similar to pV* da?. 

 Thus, to integrate # 4 (log e x}-, put log e x = y. 

 Then x = e v and dx = e v dy 



and (a^lo&a:) 2 ete = U 4v t/ 2 e" dy 



2 



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 125 



2 2 



