Question

高数分部积分法

为什么d1/2x变成dx了
是公式要求的吗

Answer 1

这一步有个变形过程，希望能帮到你，望采纳哦

Answer 2

1+cosx = 2[cos(x/2)]^2
∫(0->π/2) x/(1+cosx ) dx
=(1/2)∫(0->π/2) x[sec(x/2)]^2 dx
=∫(0->π/2) x dtan(x/2)
=[xtan(x/2)]|(0->π/2) - ∫(0->π/2) tan(x/2) dx
=π/4 - ∫(0->π/2) sin(x/2)/cos(x/2) dx
=π/4 +2 ∫(0->π/2) dcos(x/2)/cos(x/2)
=π/4 +2 [ln|cos(x/2)|]|(0->π/2)
=π/4 +2ln(1/√2)
=π/4 -ln2

Answer 3

不定积分结果不唯一求导验证应该能够提高凑微分的计算能力