求不定积分∫1/x√（x^2/9-1）dx - 知识问答

求不定积分∫1/x√（x^2/9-1）dx

1个回答

令x=3sect,则dx=3secttantdt,t=arccos(3/x)
∫1/x√（x^2/9-1）dx
=∫1/(3sect*tant)*3secttantdt
=∫1dt
=t+C
=arccos(3/x)+C

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