Solve ∫ 3t²/(1+t²) dt?

Question

could you tell me how to select best answer? thanks (:

Answer 1

∫ 3t²/(1+t²) dt

∫ 3(t²+1)-3/(1+t²) dt

= 3∫(1+ t²)/(1+t²) dt - ∫ 3/(1+t²) dt

=3t -[3/2 ∫ 2/(1+t²) dt] =   3t - (3/2) log(1+t²) +c    answer

c = constant

Answer 2

3t² / (t² + 1) = 3 - 3 / (t² + 1)

I = ∫ 3 dt - 3 ∫ dt / (t² + 1)

I = 3 t - 3 tan^(-1) t + C

Answer 3

=3∫ dt-3∫ 1/(1+t²)dt=

3t-3arctant+C