`int(xtan^-1x)/(1+x^2)^(3/2)dx`A. `(tan^(-1)x)/(sqrt(1+x^(2)))-(x)/(sqrt(1+x^(2)))+C`B. `(-tan^(-1)x)/(sqrt(1+x^(2)))+(x)/(sqrt(1+x^(2)))+C`C. `(xtan^(-1)x)/(sqrt(1+x^(2)))+(1)/(2)log|(x)/(sqrt(1+x^(2)))|+C`D. none of these

`int(xtan^-1x)/(1+x^2)^(3/2)dx`A. `(tan^(-1)x)/(sqrt(1+x^(2)))-(x)/(sq

1.	`int(xtan^-1x)/(1+x^2)^(3/2)dx`A. `(tan^(-1)x)/(sqrt(1+x^(2)))-(x)/(sqrt(1+x^(2)))+C`B. `(-tan^(-1)x)/(sqrt(1+x^(2)))+(x)/(sqrt(1+x^(2)))+C`C. `(xtan^(-1)x)/(sqrt(1+x^(2)))+(1)/(2)log\|(x)/(sqrt(1+x^(2)))\|+C`D. none of these
Answer» Correct Answer - B Put x=tan t, so that dx `=sec^(2)tdtandt=tan^(-1)x`. `:." "I=int(t(tant))/((1+tan^(2)t)^((3)/(2)))sec^(2)tdt=intunderset(I)(t)underset(II)(sin)tdt`.