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

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

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integral of (20)/(x+5)

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

20 ln ∣ x + 5 ∣ + C

Solution steps

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

Take the constant out:

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

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

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 = x + 5

= 20 ln ∣ x + 5 ∣

Add a constant to the solution

= 20 ln ∣ x + 5 ∣ + C

(2, 1), (8, 7)

(f (x))^{g (x)}

e^{- \frac{x}{2}} 0

f (x) = ln (x + x^{2} + 1)

\frac{d}{d x} (x^{2} sin (x) + 2)