What is the integral of 1/(1+14x) ?

The integral of 1/(1+14x) is 1/14 ln|1+14x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(1+14x)

\int \frac{1}{1 + 14 x} d x

\frac{1}{14} ln ∣ 1 + 14 x ∣ + C

Solution steps

\int \frac{1}{1 + 14 x} d x

Apply u-substitution

= \int \frac{1}{14 u} d u

Take the constant out:

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

= \frac{1}{14} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{14} ln ∣ u ∣

Substitute back

u = 1 + 14 x

= \frac{1}{14} ln ∣ 1 + 14 x ∣

Add a constant to the solution

= \frac{1}{14} ln ∣ 1 + 14 x ∣ + C

f (x) = 4 x + 1

x \to 0 lim (\frac{( 2 + x ) ^{2} - 4}{x})

\frac{d}{d x} (arccos (\frac{9}{x}))

\frac{\partial}{\partial y} (x y - z)

\frac{d ^{2}}{d x ^{2}} (e^{\frac{4}{x}})

What is the integral of 1/(1+14x) ?
The integral of 1/(1+14x) is 1/14 ln|1+14x|+C