What is the integral of tan(x/4) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of tan(x/4)

\int tan (\frac{x}{4}) d x

- 4 ln cos (\frac{x}{4}) + C

Solution steps

\int tan (\frac{x}{4}) d x

Rewrite using trig identities

= \int \frac{sin ( \frac{x}{4} )}{cos ( \frac{x}{4} )} d x

Apply u-substitution

: \int - \frac{4}{u} d u

= \int - \frac{4}{u} d u

Take the constant out:

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

= - 4 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 4 ln ∣ u ∣

Substitute back

u = cos (\frac{x}{4})

= - 4 ln cos (\frac{x}{4})

Add a constant to the solution

= - 4 ln cos (\frac{x}{4}) + C

\frac{a}{1 - b x}

\frac{d y}{d x} - 5 y = x^{2}

\frac{7}{x}, - 1

y^{^{'}} + 4 y = 1, y (0) = 1

f (x) = x^{2} + 16, at x = - 3