What is the integral of (sec(θ))/(sec(θ)-cos(θ)) ?

The integral of (sec(θ))/(sec(θ)-cos(θ)) is -cot(θ)+C

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integral of (sec(θ))/(sec(θ)-cos(θ))

\int \frac{sec ( θ )}{sec ( θ ) - cos ( θ )} d θ

- cot (θ) + C

Solution steps

\int \frac{sec ( θ )}{sec ( θ ) - cos ( θ )} d θ

Rewrite using trig identities

= \int \frac{1}{1 - cos ^{2} ( θ )} d θ

Rewrite using trig identities

= \int csc^{2} (θ) d θ

Use the common integral:

\int csc^{2} (θ) d θ = - cot (θ)

= - cot (θ)

Add a constant to the solution

= - cot (θ) + C

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What is the integral of (sec(θ))/(sec(θ)-cos(θ)) ?
The integral of (sec(θ))/(sec(θ)-cos(θ)) is -cot(θ)+C