Evaluate the integral by multiplying by a form of 1 and using a substitution (if necessary) to reduce it to standard form.

Question

∫ 1/1-sinx dx

A) tanx - secx + C

B) tanx + secx+ C

C) -cotx - cscx+ C

D) cotx + cscx+ C

Answer 1

Multiply by (1 + sin(x))/(1 + sin(x)) to get ∫(1 + sin(x))/cos²(x) dx then split the integral into 2 pieces making:

∫sec²(x) dx + ∫tan(x)sec(x) dx

These are both standard trig integrals and result in tan(x) + sec(x) + C