Question

=∫2t^2/(1+t^2)dt=2(∫dt-∫1/(1+t^2)dt) 这不不懂

Answer 1

2t^2/(1+t^2)=[2(1+t^2)-2]/(1+t^2)=2-2/(1+t^2)

于是 ∫2t^2/(1+t^2)dt=∫(2-2/(1+t^2))dt=∫2dt-∫2/(1+t^2)dt=2(∫dt-∫1/(1+t^2)dt)