What is the integral of (x^2)/(-7+x^3) ?

The integral of (x^2)/(-7+x^3) is 1/3 ln|-7+x^3|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x^2)/(-7+x^3)

\int \frac{x ^{2}}{- 7 + x ^{3}} d x

\frac{1}{3} ln - 7 + x^{3} + C

Solution steps

\int \frac{x ^{2}}{- 7 + x ^{3}} d x

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 = - 7 + x^{3}

= \frac{1}{3} ln - 7 + x^{3}

Add a constant to the solution

= \frac{1}{3} ln - 7 + x^{3} + C

What is the integral of (x^2)/(-7+x^3) ?
The integral of (x^2)/(-7+x^3) is 1/3 ln|-7+x^3|+C