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

= \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

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

y = x^{2} + 3, (- 5, 28)

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

\int x^{2} a^{2} + a^{2} x^{2} d x

\frac{d}{d x} (sec (x) + tan (x))

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