What is the integral of int (1-sinx)/(cosx) dx?

1 Answer
Jim H
Feb 24, 2016

(1-sinx)/cosx = ((1-sinx))/cosx * ((1+sinx))/((1+sinx))

= (1-sin^2x)/(cosx(1+sinx))

= cos^2x/(cosx(1+sinx))

= cosx/(1+sinx)

int (1-sinx)/cosx dx = int cosx/(1+sinx) dx

= ln(1+sinx)+C

(by substitution with u=1+sinx)

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