∫1/sinxdx等于多少,要过程 谢
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∫1/sinxdx等于多少,要过程 谢
![∫1/sinxdx等于多少,要过程 谢](/uploads/image/z/20127934-46-4.jpg?t=%E2%88%AB1%2Fsinxdx%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%2C%E8%A6%81%E8%BF%87%E7%A8%8B+%E8%B0%A2)
∫1/sinxdx=∫sinx/sin^2xdx
=-∫dcosx/(1-cos^2x)
=-∫dt/(1-t^2)[令t=cosx]
=-1/2∫(1/(t+1)-1/(t-1))dt
=-1/2(ln|t+1|-ln|t-1|)+C
=-1/2ln|(cosx+1)/(cosx-1)|+C
=-∫dcosx/(1-cos^2x)
=-∫dt/(1-t^2)[令t=cosx]
=-1/2∫(1/(t+1)-1/(t-1))dt
=-1/2(ln|t+1|-ln|t-1|)+C
=-1/2ln|(cosx+1)/(cosx-1)|+C