What is the integral of 9x^2ln(x) ?

The integral of 9x^2ln(x) is 3x^3ln(x)-x^3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 9x^2ln(x)

\int 9 x^{2} ln (x) d x

3 x^{3} ln (x) - x^{3} + C

Solution steps

\int 9 x^{2} ln (x) d x

Take the constant out:

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

= 9 \cdot \int x^{2} ln (x) d x

Apply Integration By Parts

= 9 (\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x)

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= 9 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9})

Simplify

9 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) : 3 x^{3} ln (x) - x^{3}

= 3 x^{3} ln (x) - x^{3}

Add a constant to the solution

= 3 x^{3} ln (x) - x^{3} + C

What is the integral of 9x^2ln(x) ?
The integral of 9x^2ln(x) is 3x^3ln(x)-x^3+C