神马作文网高数,不定积分题
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高数,不定积分题
令x=a*secy,dx=a*secy*tany dy,假设x>a
cosy=a/x,siny=√(x²-a²) / x,tany=√(x²-a²) / a
∫[√(x²-a²) / x] dx
= ∫[√(a²*sec²y - a²) / (a*secy)] * (a*secy*tany) dy
= ∫[(a*tany) / (a*secy)] * (a*secy*tany) dy
= a*∫tan²y dy
= a*∫(sec²y-1) dy
= a*(tany-y) + C
= a*√(x²-a²) / a - a*arcsec(x/a) + C
= √(x²-a²) - a*arcsec(x/a) + C
cosy=a/x,siny=√(x²-a²) / x,tany=√(x²-a²) / a
∫[√(x²-a²) / x] dx
= ∫[√(a²*sec²y - a²) / (a*secy)] * (a*secy*tany) dy
= ∫[(a*tany) / (a*secy)] * (a*secy*tany) dy
= a*∫tan²y dy
= a*∫(sec²y-1) dy
= a*(tany-y) + C
= a*√(x²-a²) / a - a*arcsec(x/a) + C
= √(x²-a²) - a*arcsec(x/a) + C