What is the integral of (100)/(7x-16) ?

The integral of (100)/(7x-16) is 100/7 ln|7x-16|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (100)/(7x-16)

\int \frac{100}{7 x - 16} d x

\frac{100}{7} ln ∣ 7 x - 16 ∣ + C

Solution steps

\int \frac{100}{7 x - 16} d x

Take the constant out:

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

= 100 \cdot \int \frac{1}{7 x - 16} d x

Apply u-substitution

= 100 \cdot \int \frac{1}{7 u} d u

Take the constant out:

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

= 100 \cdot \frac{1}{7} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 100 \cdot \frac{1}{7} ln ∣ u ∣

Substitute back

u = 7 x - 16

= 100 \cdot \frac{1}{7} ln ∣ 7 x - 16 ∣

Simplify

100 \cdot \frac{1}{7} ln ∣ 7 x - 16 ∣ : \frac{100}{7} ln ∣ 7 x - 16 ∣

= \frac{100}{7} ln ∣ 7 x - 16 ∣

Add a constant to the solution

= \frac{100}{7} ln ∣ 7 x - 16 ∣ + C

What is the integral of (100)/(7x-16) ?
The integral of (100)/(7x-16) is 100/7 ln|7x-16|+C