i got the ans to that question jus lemme know if i am rite

 

integral will be represented as  {

 

0 to 1{2[ tan-1 x ]^2dx  [put x=tany]

 

 =2{y^2 sec^2 y dy

 

 =then integrate this by parts and the second part u will get 0 to pi/4 2{tany y dy

here u can replace back y for tan-1 x and change the limits to 0 to 1 and then solve the integral again by parts

and u will get the ans ......

please try it i am sure u will get

 

please lemme now if i am correct....i cudnt write down the whole solution here but i have tried to be as clear as possible...please help....

 

i gues u will get this ans=(pi^2-8pi+16)/8