Question

1/sinx的不定积分是多少?麻烦给个过程

Answer 1

∫ dx/sinx

=∫ dx/(2*sin(x/2)*cos(x/2))

=∫ d(x/2)/(sin(x/2)*cos(x/2))

=∫ (d(x/2)/cos^2(x/2)) / (sin(x/2)/cos(x/2))

=∫ d(tan(x/2)) / tan(x/2)

=ln | tan(x/2) | +C

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