u = atant
du = 1/(1+t^2) dt

= udt

so it is (u^2)/2 or (atan t)^2 / 2

>>42175
= u du (not udt)

Its Arctangent^2(t) all over 2 + c

or alternatively, arctangent^2(t) times (1/2) + c

>>42175
>forgetting your constant of integration

end
yourself