Integrate : x tan^-1 x / square root (1+x^2)

Answers (1)

Solution:   We have 

                      I=int fracx	an^-1xsqrt1+x^2dx

        Integrating by parts  , we get 

         u=	an^-1x Rightarrow du=fracdx1+x^2;v=sqrt1+x^2Rightarrow dv=fracxdxsqrt1+x^2\ \ Rightarrow hspace1cmI=sqrt1+x^2	an^-1x-int sqrt1+x^2 cdot fracdx1+x^2\ \ Rightarrow hspace1cmI=sqrt1+x^2	an^-1x-ln (x+sqrtx^2+1)+C

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