What is the integral of (20)/(q+5) ?

The integral of (20)/(q+5) is 20ln|q+5|+C

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integral of (20)/(q+5)

\int \frac{20}{q + 5} d q

20 ln ∣ q + 5 ∣ + C

Solution steps

\int \frac{20}{q + 5} d q

Take the constant out:

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

= 20 \cdot \int \frac{1}{q + 5} d q

Apply u-substitution

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

= 20 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 20 ln ∣ u ∣

Substitute back

u = q + 5

= 20 ln ∣ q + 5 ∣

Add a constant to the solution

= 20 ln ∣ q + 5 ∣ + C

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