What is the integral of-1/(cos(x)) ?

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

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integral of-1/(cos(x))

\int - \frac{1}{cos ( x )} d x

- ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int - \frac{1}{cos ( x )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{cos ( x )} d x

Rewrite using trig identities

= - \int sec (x) d x

Use the common integral:

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

= - ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= - ln ∣ tan (x) + sec (x) ∣ + C

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