What is the integral of (50)/(x+5) ?

The integral of (50)/(x+5) is 50ln|x+5|+C

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integral of (50)/(x+5)

\int \frac{50}{x + 5} d x

50 ln ∣ x + 5 ∣ + C

Solution steps

\int \frac{50}{x + 5} d x

Take the constant out:

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

= 50 \cdot \int \frac{1}{x + 5} d x

Apply u-substitution

= 50 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 50 ln ∣ u ∣

Substitute back

u = x + 5

= 50 ln ∣ x + 5 ∣

Add a constant to the solution

= 50 ln ∣ x + 5 ∣ + C

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