What is the integral of (s^2)/(s^3+5) ?

The integral of (s^2)/(s^3+5) is 1/3 ln|s^3+5|+C

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integral of (s^2)/(s^3+5)

\int \frac{s ^{2}}{s ^{3} + 5} d s

\frac{1}{3} ln s^{3} + 5 + C

Solution steps

\int \frac{s ^{2}}{s ^{3} + 5} d s

Apply u-substitution

= \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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} ln ∣ u ∣

Substitute back

u = s^{3} + 5

= \frac{1}{3} ln s^{3} + 5

Add a constant to the solution

= \frac{1}{3} ln s^{3} + 5 + C

\int_{0}^{1} 2 x^{2} d x

\int \frac{1}{x ^{2} - 2 x - 8} d x

\frac{d}{d x} (ln (\frac{1}{6 x}))

d er i v a t i v e f (x) = 7 tan (x^{4})

d er i v a t i v e 70 π t + 35 cos (\frac{- 2 π t - π}{2})

What is the integral of (s^2)/(s^3+5) ?
The integral of (s^2)/(s^3+5) is 1/3 ln|s^3+5|+C