∫(cosx^2/sinx^3)dx
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![∫(cosx^2/sinx^3)dx](/uploads/image/z/8746919-71-9.jpg?t=%E2%88%AB%28cosx%5E2%2Fsinx%5E3%29dx)
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∫(cosx^2/sinx^3)dx
∫(cosx^2/sinx^3)dx
∫(cosx^2/sinx^3)dx
∫ sin²x/cos³x dx
= ∫ tan²xsecx dx
= ∫ (sec²x - 1)secx dx
= ∫ sec³x dx - ∫ secx dx
对于∫ sec³x dx = ∫ secx d(tanx)
= secxtanx - ∫ tanx d(secx)
= secxtanx - ∫ tanx(secxtanx) dx
= secxtanx - ∫ (sec²x - 1)secx dx
= secxtanx - ∫ sec³x dx + ∫ secx dx
2∫ sec³x dx = secxtanx + ∫ secx dx
∫ sec³x dx = (1/2)secxtanx + (1/2)∫ secx dx
∫ sin²x/cos³x dx = (1/2)secxtanx + (1/2 - 1)∫ secx dx
= (1/2)secxtanx - (1/2)ln| secx + tanx | + C
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