What is the integral of 2sec(x) ?

The integral of 2sec(x) is 2ln|tan(x)+sec(x)|+C

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integral of 2sec(x)

\int 2 sec (x) d x

2 ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int 2 sec (x) d x

Take the constant out:

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

= 2 \cdot \int sec (x) d x

Use the common integral:

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

= 2 ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= 2 ln ∣ tan (x) + sec (x) ∣ + C

(5, - 3), (- 9, - 6)

\int \frac{3 cos ( x )}{sin ^{2} ( x )} d x

tan (x) + \frac{cos ( x )}{1 + sin ( x )}

\frac{d}{d x} (\frac{x - y}{x})

\int - \frac{1}{2} e^{y} sin (y) d y

What is the integral of 2sec(x) ?
The integral of 2sec(x) is 2ln|tan(x)+sec(x)|+C