Question

大学高数求不定积分

Answer 1

∫sin²x/cos³xdx
=∫(sinxtanx)/cos²xdx
=∫(sinxtanx)d(tanx)
=(1/2)∫sinxd(tan²x)
=(1/2)sinxtan²x+(1/2)∫tan²xd(sinx)
=(1/2)sinxtan²x+(1/2)∫sin²x/cosxdx
=(1/2)sinxtan²x+(1/2)∫(1-cos²x)/cosxdx
=(1/2)sinxtan²x+(1/2)∫(1/cosx-cosx)dx
=(1/2)sinxtan²x-(1/2)sinx+(1/2)∫(1/cosx)dx
=(1/2)sinxtan²x-(1/2)sinx+(1/2)(ln|secx+tanx|)+C

追问

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