Evaluate the integral. \frac{1-\sin x}{\cos x}dx

Cheyanne Leigh

Cheyanne Leigh

Answered question

2021-11-07

Evaluate the integral.
1sinxcosxdx

Answer & Explanation

SoosteethicU

SoosteethicU

Skilled2021-11-08Added 102 answers

Given,
1sinxcosxdx
On simplification, we get
1sinxcosxdx=(1cosxsinxcosx)
=(secxtanx)dx
=ln|secx+tanx|ln|secx|+C
=ln|secx+tanxsecx|+C
=ln|1+tanxsecx|+C
=ln|1+sinxcosx1cosx|+C
=ln|1+sinx|+C

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