What is the integral of-sec(x) ?

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

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integral of-sec(x)

\int - sec (x) d x

- ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int - sec (x) d x

Take the constant out:

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

= - \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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\int y^{6} d y

y y^{^{'}} = x (1 + y^{2})