Question

高等数学。定积分。中间划线的怎么变得？

Answer 1

令2t/(1+t)(1+t²)=(Ax+B)/(1+t²)+C/(1+t)

待定系数求出A、B、C
——————————————
∫(1+t)/(1+t²) dt=∫1/(1+t²)dt + ∫ t/(1+t²) dt
=arctant+(1/2)*∫ 1/(1+t²) dt²
=arctanx+(1/2)*ln(1+t²)+C

Answer 2

分解因式 变成
(1/1+t^2)+(t/1+t^2)-(1/1+t)=arctant+二分之一*ln(1+t^2)-ln(1+t)

Answer 3

=∫(0→1)[1/(1+t²)+t/(1+t²)-1/(1+t)]dt
=[arctant+1/2·ln(1+t²)-ln(1+t²)] |(0→1)
=[arctant+1/2·ln(1+t²)/(1+t)²] |(0→1)

追答

=∫(0→1)[1/(1+t²)+t/(1+t²)-1/(1+t)]dt
=[arctant+1/2·ln(1+t²)-ln(1+t)] |(0→1)
【前面这里打错了，更正一下】
=[arctant+1/2·ln(1+t²)/(1+t)²] |(0→1)