Question Number 101816 by Dwaipayan Shikari last updated on 04/Jul/20

∫_1 ^( e) (((tan^(−1) x)/x)+((log)/(x^2 +1)))dx

Answered by Ar Brandon last updated on 05/Jul/20

Let I=∫_1 ^e {((tan^(−1) x)/x)+((logx)/(x^2 +1))}dx (d/dx){tan^(−1) x∙logx}=((tan^(−1) x)/x)+((logx)/(1+x^2 )) ⇒I=∫_1 ^e d(tan^(−1) x∙logx)=[tan^(−1) x∙logx]_1 ^e =tan^(−1) (e)