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

The integral of 1/2 tan(2x) is -1/4 ln|cos(2x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/2 tan(2x)

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

- \frac{1}{4} ln ∣ cos (2 x) ∣ + C

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int tan (2 x) d x

Rewrite using trig identities

= \frac{1}{2} \cdot \int \frac{sin ( 2 x )}{cos ( 2 x )} d x

Apply u-substitution

: \int - \frac{1}{2 u} d u

= \frac{1}{2} \cdot \int - \frac{1}{2 u} d u

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} (- \frac{1}{2} ln ∣ u ∣)

Substitute back

u = cos (2 x)

= \frac{1}{2} (- \frac{1}{2} ln ∣ cos (2 x) ∣)

Simplify

\frac{1}{2} (- \frac{1}{2} ln ∣ cos (2 x) ∣) : - \frac{1}{4} ln ∣ cos (2 x) ∣

= - \frac{1}{4} ln ∣ cos (2 x) ∣

Add a constant to the solution

= - \frac{1}{4} ln ∣ cos (2 x) ∣ + C

\frac{d}{d x} (sin (cos (cot (3 π x))))

\frac{d}{d x} (\frac{1}{5 - 4 e ^{x}})

\int \frac{2}{x ^{4} - 1} d x

x \to 4 lim (9)

x \to 0 + lim (\frac{x}{1 + x})

What is the integral of 1/2 tan(2x) ?
The integral of 1/2 tan(2x) is -1/4 ln|cos(2x)|+C