What is the integral of (x^2)/(5x^3+8) ?

The integral of (x^2)/(5x^3+8) is 1/15 ln|5x^3+8|+C

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integral of (x^2)/(5x^3+8)

\int \frac{x ^{2}}{5 x ^{3} + 8} d x

\frac{1}{15} ln 5 x^{3} + 8 + C

Solution steps

\int \frac{x ^{2}}{5 x ^{3} + 8} d x

Apply u-substitution

: \int \frac{1}{15 u} d u

= \int \frac{1}{15 u} d u

Take the constant out:

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

= \frac{1}{15} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{15} ln ∣ u ∣

Substitute back

u = 5 x^{3} + 8

= \frac{1}{15} ln 5 x^{3} + 8

Add a constant to the solution

= \frac{1}{15} ln 5 x^{3} + 8 + C

f (x) = 3 e^{x} + x, (0, 3)

\int (7 x (x^{6} - \frac{1}{7})) d x

\frac{1}{( s ^{2} + 5 )}

f (x) = \frac{1 - 4 x}{1 + 4 x}

\frac{\partial}{\partial y} (4 x^{3} y^{3} + 2)

What is the integral of (x^2)/(5x^3+8) ?
The integral of (x^2)/(5x^3+8) is 1/15 ln|5x^3+8|+C