What is the integral of 3sec(2x) ?

The integral of 3sec(2x) is 3/2 ln|tan(2x)+sec(2x)|+C

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integral of 3sec(2x)

\int 3 sec (2 x) d x

\frac{3}{2} ln ∣ tan (2 x) + sec (2 x) ∣ + C

Solution steps

\int 3 sec (2 x) d x

Take the constant out:

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

= 3 \cdot \int sec (2 x) d x

Apply u-substitution

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

= 3 \cdot \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

= 3 \cdot \frac{1}{2} \cdot \int sec (u) d u

Use the common integral:

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

= 3 \cdot \frac{1}{2} ln ∣ tan (u) + sec (u) ∣

Substitute back

u = 2 x

= 3 \cdot \frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣

Simplify

3 \cdot \frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣ : \frac{3}{2} ln ∣ tan (2 x) + sec (2 x) ∣

= \frac{3}{2} ln ∣ tan (2 x) + sec (2 x) ∣

Add a constant to the solution

= \frac{3}{2} ln ∣ tan (2 x) + sec (2 x) ∣ + C

f (4) = - 7 x^{2} + 2 x

\frac{d}{d x} (arctan (\frac{3 x - 8}{x ^{3}}))

x \to \infty lim (x^{6})

\frac{\partial}{\partial y} (2 + x^{2} + y^{2})

x sin (- 2 x), at π

What is the integral of 3sec(2x) ?
The integral of 3sec(2x) is 3/2 ln|tan(2x)+sec(2x)|+C