Integrating 2t^2/(1+t^2)^2 with Trig Substitution

[Litcyb]

Homework Statement

integrate 2t^(2)/(1+t^2)^(2)

Homework Equations

trig sub 1+tan^2(x)= sec^2(x)

The Attempt at a Solution

the attempted solution is attached.

 

[ehild]

Your derivation is not correct and the method you follow is a bit complicated. Try integration by parts, ∫u'vdt=uv-∫uv'dt, with u'=2t/(1+t^2)^2 and v=t.

ehild

 

[SteamKing]

If y = (1/3)t + C, then dy/dt = 1/3, which is clearly not even remotely close to the original integrand.

 

[Litcyb]

omg! i knowwwwwwwwwwwwwwwwww! i did it. that was so stupid of me. thank you.