integrate 10

this is integral 2 (tan^-1x)²

let taninverse x=t
this implies tan t=x
this implies sec²t dt=dx
i.e (1+tan²t)dt=dx

therefore given integral becomes 2t²(1+tan²t)dt
=2t²dt+2t²tan²t dt
2t²tan²dt can be evaluated by using integration by parts.

i think this solves the major part.

and dude dont forget to change the limits accordingly.

dude please solve it completely for me.

ok solving it completely

2t²dt = 2t³/3

∫ 2t²tan²tdt=2t²(∫ (sec²t -1))+∫4t(∫(sec²t -1)) dt

= 2t²tant-2t³/3 +4t tant -4t²

now u give th e limits.

bye the way anyone check if this can be solved by basic formulae of definite integrals.

you need to integrate 4t tant- 4t² also.

ya sorry forgot that. anyways again use integration by parts for 4t tant

4t log|sect| - ∫4log|sect| how to move from here?

no idea dude. then i think my approach was wrong

done this before....

see this....
"http://targetiit.com/iit_jee_forum/posts/def_2192.html"