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Popular >

integral of sec(x)-1

Solution

\int sec (x) - 1 d x

Solution

ln ∣ tan (x) + sec (x) ∣ - x + C

Solution steps

\int sec (x) - 1 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 1 d x

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

\int 1 d x = x

= ln ∣ tan (x) + sec (x) ∣ - x

Add a constant to the solution

= ln ∣ tan (x) + sec (x) ∣ - x + C

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\frac{1}{s ^{2} + \frac{s}{4}}

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\int 3 x^{2} + 6 d x

Frequently Asked Questions (FAQ)

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