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

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

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integral of (x^2)/(3-x^3)

\int \frac{x ^{2}}{3 - x ^{3}} d x

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

Solution steps

\int \frac{x ^{2}}{3 - x ^{3}} 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 = 3 - x^{3}

= - \frac{1}{3} ln 3 - x^{3}

Add a constant to the solution

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

1500 x + 3000 (5 x + 3)^{- 1} - 1000

\frac{e ^{- 4 s}}{s}

\int_{0}^{\frac{5}{4}} \frac{1}{25 + 16 x ^{2}} d x

\frac{d}{d x} (y ln (x))

y = \frac{4 ln ( 3 x )}{5 + 2 x}

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