高数不定积分∫secxdx∫secxdx=∫(1/cosx)dx=∫[cosx/(cosx)^2]dx=∫[1/1-(sinx)^2]d(sinx)=(1/2)∫[1/(1-sinx)+1/(1+sinx)]d(sinx)=(1/2)[-ln|1-sinx|+ln|1+sinx|]+C(这里为什么变成-ln|1-sinx|,负号哪里来的么看懂=(1/2)ln|(1+sinx)/(1
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![高数不定积分∫secxdx∫secxdx=∫(1/cosx)dx=∫[cosx/(cosx)^2]dx=∫[1/1-(sinx)^2]d(sinx)=(1/2)∫[1/(1-sinx)+1/(1+sinx)]d(sinx)=(1/2)[-ln|1-sinx|+ln|1+sinx|]+C(这里为什么变成-ln|1-sinx|,负号哪里来的么看懂=(1/2)ln|(1+sinx)/(1](/uploads/image/z/11949096-48-6.jpg?t=%E9%AB%98%E6%95%B0%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%E2%88%ABsecxdx%E2%88%ABsecxdx%3D%E2%88%AB%281%2Fcosx%29dx%3D%E2%88%AB%5Bcosx%2F%28cosx%29%5E2%5Ddx%3D%E2%88%AB%5B1%2F1-%28sinx%29%5E2%5Dd%28sinx%29%3D%281%2F2%29%E2%88%AB%5B1%2F%281-sinx%29%2B1%2F%281%2Bsinx%29%5Dd%28sinx%29%3D%281%2F2%29%5B-ln%7C1-sinx%7C%2Bln%7C1%2Bsinx%7C%5D%2BC%EF%BC%88%E8%BF%99%E9%87%8C%E4%B8%BA%E4%BB%80%E4%B9%88%E5%8F%98%E6%88%90-ln%7C1-sinx%7C%2C%E8%B4%9F%E5%8F%B7%E5%93%AA%E9%87%8C%E6%9D%A5%E7%9A%84%E4%B9%88%E7%9C%8B%E6%87%82%3D%281%2F2%29ln%7C%281%2Bsinx%29%2F%281)
高数不定积分∫secxdx∫secxdx=∫(1/cosx)dx=∫[cosx/(cosx)^2]dx=∫[1/1-(sinx)^2]d(sinx)=(1/2)∫[1/(1-sinx)+1/(1+sinx)]d(sinx)=(1/2)[-ln|1-sinx|+ln|1+sinx|]+C(这里为什么变成-ln|1-sinx|,负号哪里来的么看懂=(1/2)ln|(1+sinx)/(1
高数不定积分∫secxdx
∫secxdx
=∫(1/cosx)dx
=∫[cosx/(cosx)^2]dx
=∫[1/1-(sinx)^2]d(sinx)
=(1/2)∫[1/(1-sinx)+1/(1+sinx)]d(sinx)
=(1/2)[-ln|1-sinx|+ln|1+sinx|]+C(这里为什么变成-ln|1-sinx|,负号哪里来的么看懂
=(1/2)ln|(1+sinx)/(1-sinx)|+C
=ln|secx+tanx|+C
高数不定积分∫secxdx∫secxdx=∫(1/cosx)dx=∫[cosx/(cosx)^2]dx=∫[1/1-(sinx)^2]d(sinx)=(1/2)∫[1/(1-sinx)+1/(1+sinx)]d(sinx)=(1/2)[-ln|1-sinx|+ln|1+sinx|]+C(这里为什么变成-ln|1-sinx|,负号哪里来的么看懂=(1/2)ln|(1+sinx)/(1
∫1/(1-sinx) d(sinx)=-∫1/(1-sinx) d(1-sinx)
=-ln|1-sinx|+C
dsinx----→d(1-sinx)差一个负号啊。
dsinx----→d(1+sinx)就是相等的