What is the integral of 4/(100+2x) ?

The integral of 4/(100+2x) is 2ln|100+2x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4/(100+2x)

\int \frac{4}{100 + 2 x} d x

2 ln ∣ 100 + 2 x ∣ + C

Solution steps

\int \frac{4}{100 + 2 x} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{100 + 2 x} d x

Apply u-substitution

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

= 4 \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

= 4 \cdot \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 4 \cdot \frac{1}{2} ln ∣ u ∣

Substitute back

u = 100 + 2 x

= 4 \cdot \frac{1}{2} ln ∣ 100 + 2 x ∣

Simplify

4 \cdot \frac{1}{2} ln ∣ 100 + 2 x ∣ : 2 ln ∣ 100 + 2 x ∣

= 2 ln ∣ 100 + 2 x ∣

Add a constant to the solution

= 2 ln ∣ 100 + 2 x ∣ + C

\int 2 x^{2} + 4 x - 6 d x

\int \frac{ln ( x - 3 )}{x - 3} d x

\int \frac{x ^{2} + x + 1}{x ^{3} + x} d x

\int e^{x} (2 x + 5) d x

\int \frac{cos ( 2 x )}{x ^{4}} d x

What is the integral of 4/(100+2x) ?
The integral of 4/(100+2x) is 2ln|100+2x|+C