What is the integral of-4/(s+1) ?

The integral of-4/(s+1) is -4ln|s+1|+C

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integral of-4/(s+1)

\int - \frac{4}{s + 1} d s

- 4 ln ∣ s + 1 ∣ + C

Solution steps

\int - \frac{4}{s + 1} d s

Take the constant out:

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

= - 4 \cdot \int \frac{1}{s + 1} d s

Apply u-substitution

= - 4 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 4 ln ∣ u ∣

Substitute back

u = s + 1

= - 4 ln ∣ s + 1 ∣

Add a constant to the solution

= - 4 ln ∣ s + 1 ∣ + C

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