What is the integral of 1/(cos(u)) ?

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

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integral of 1/(cos(u))

\int \frac{1}{cos ( u )} d u

ln ∣ tan (u) + sec (u) ∣ + C

Solution steps

\int \frac{1}{cos ( u )} d u

Rewrite using trig identities

= \int sec (u) d u

Use the common integral:

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

= ln ∣ tan (u) + sec (u) ∣

Add a constant to the solution

= ln ∣ tan (u) + sec (u) ∣ + C

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