What is the integral of (12)/(2x+50) ?

The integral of (12)/(2x+50) is 6ln|2x+50|+C

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integral of (12)/(2x+50)

\int \frac{12}{2 x + 50} d x

6 ln ∣ 2 x + 50 ∣ + C

Solution steps

\int \frac{12}{2 x + 50} d x

Take the constant out:

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

= 12 \cdot \int \frac{1}{2 x + 50} d x

Apply u-substitution

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

= 12 \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

= 12 \cdot \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 12 \cdot \frac{1}{2} ln ∣ u ∣

Substitute back

u = 2 x + 50

= 12 \cdot \frac{1}{2} ln ∣ 2 x + 50 ∣

Simplify

12 \cdot \frac{1}{2} ln ∣ 2 x + 50 ∣ : 6 ln ∣ 2 x + 50 ∣

= 6 ln ∣ 2 x + 50 ∣

Add a constant to the solution

= 6 ln ∣ 2 x + 50 ∣ + C

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What is the integral of (12)/(2x+50) ?
The integral of (12)/(2x+50) is 6ln|2x+50|+C