What is the integral of 1/(cos(θ)) ?

The integral of 1/(cos(θ)) is ln|tan(θ)+sec(θ)|+C

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integral of 1/(cos(θ))

\int \frac{1}{cos ( θ )} d θ

ln ∣ tan (θ) + sec (θ) ∣ + C

Solution steps

\int \frac{1}{cos ( θ )} d θ

Rewrite using trig identities

= \int sec (θ) d θ

Use the common integral:

\int sec (θ) d θ = ln ∣ tan (θ) + sec (θ) ∣

= ln ∣ tan (θ) + sec (θ) ∣

Add a constant to the solution

= ln ∣ tan (θ) + sec (θ) ∣ + C

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What is the integral of 1/(cos(θ)) ?
The integral of 1/(cos(θ)) is ln|tan(θ)+sec(θ)|+C