What is the integral of 1/(sec(2x)) ?

The integral of 1/(sec(2x)) is 1/2 sin(2x)+C

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integral of 1/(sec(2x))

\int \frac{1}{sec ( 2 x )} d x

\frac{1}{2} sin (2 x) + C

Solution steps

\int \frac{1}{sec ( 2 x )} d x

Rewrite using trig identities

= \int cos (2 x) d x

Apply u-substitution

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

= \int cos (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 cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{2} sin (u)

Substitute back

u = 2 x

= \frac{1}{2} sin (2 x)

Add a constant to the solution

= \frac{1}{2} sin (2 x) + C

x \to 11 + lim (x - 11)

\frac{d y}{d x} = sin (2 x) - \frac{1}{2} sin (4 x)

f (x) = x (1 - 2 x)^{3}, (1, - 1)

\frac{\partial}{\partial w} (\frac{1}{2 v - w})

\int cosh^{3} (x) d x

What is the integral of 1/(sec(2x)) ?
The integral of 1/(sec(2x)) is 1/2 sin(2x)+C