求不定积分：∫1/[x√(9-x²)]dx

求不定积分：∫1/[x√(9-x²)]dx
求不定积分：∫1/[x√(9-x²)]dx

求不定积分：∫1/[x√(9-x²)]dx
令x=3sint,则dx=3costdt
原式=∫1/(9sintcost)·3costdt
=1/3·∫csctdt
=1/3·ln|csct-cott|+C
=1/3·ln|3/x-√(3-x^2)/x|+C
=1/3·{ln[3-√(3-x^2)]-ln|x|}+C