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

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

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

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

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

Solution steps

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

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 = x^{3} + 5

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

Add a constant to the solution

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

f (t) = \frac{cos ( t )}{t ^{3}}

f (t) = sec (t)

n = 0 \sum \infty (\frac{e}{6 π})^{n}

\frac{x ^{2}}{1 - x}

y^{^{''}} + 3 y^{^{'}} - 10 y = 6 e^{4 x}

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