What is the integral of sec(x)+tan(x) ?

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

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integral of sec(x)+tan(x)

\int sec (x) + tan (x) d x

ln ∣ tan (x) + sec (x) ∣ - ln ∣ cos (x) ∣ + C

Solution steps

\int sec (x) + tan (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int tan (x) d x = - ln ∣ cos (x) ∣

= ln ∣ tan (x) + sec (x) ∣ - ln ∣ cos (x) ∣

Add a constant to the solution

= ln ∣ tan (x) + sec (x) ∣ - ln ∣ cos (x) ∣ + C

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