What is the integral of sec(2θ) ?

The integral of sec(2θ) is 1/2 ln|tan(2θ)+sec(2θ)|+C

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integral of sec(2θ)

\int sec (2 θ) d θ

\frac{1}{2} ln ∣ tan (2 θ) + sec (2 θ) ∣ + C

Solution steps

\int sec (2 θ) d θ

Apply u-substitution

: \int sec (u) \frac{1}{2} d u

= \int sec (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int sec (u) d u

Use the common integral:

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

= \frac{1}{2} ln ∣ tan (u) + sec (u) ∣

Substitute back

u = 2 θ

= \frac{1}{2} ln ∣ tan (2 θ) + sec (2 θ) ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ tan (2 θ) + sec (2 θ) ∣ + C

f (x) = 4 x^{2} - 2 x + 5

(sec^{2} (x))^{^{'}}

\int (- 4 x^{3}) d x

x \to 0 + lim (tan^{x} (9 x))

\frac{d}{d x} (π^{c o s (x)})

What is the integral of sec(2θ) ?
The integral of sec(2θ) is 1/2 ln|tan(2θ)+sec(2θ)|+C