What is the integral of 7/(3x+11) ?

The integral of 7/(3x+11) is 7/3 ln|3x+11|+C

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integral of 7/(3x+11)

\int \frac{7}{3 x + 11} d x

\frac{7}{3} ln ∣ 3 x + 11 ∣ + C

Solution steps

\int \frac{7}{3 x + 11} d x

Take the constant out:

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

= 7 \cdot \int \frac{1}{3 x + 11} d x

Apply u-substitution

: \int \frac{1}{3 u} d u

= 7 \cdot \int \frac{1}{3 u} d u

Take the constant out:

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

= 7 \cdot \frac{1}{3} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 7 \cdot \frac{1}{3} ln ∣ u ∣

Substitute back

u = 3 x + 11

= 7 \cdot \frac{1}{3} ln ∣ 3 x + 11 ∣

Simplify

7 \cdot \frac{1}{3} ln ∣ 3 x + 11 ∣ : \frac{7}{3} ln ∣ 3 x + 11 ∣

= \frac{7}{3} ln ∣ 3 x + 11 ∣

Add a constant to the solution

= \frac{7}{3} ln ∣ 3 x + 11 ∣ + C

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What is the integral of 7/(3x+11) ?
The integral of 7/(3x+11) is 7/3 ln|3x+11|+C