What is the integral of 6x^2ln(x) ?

The integral of 6x^2ln(x) is 6(1/3 x^3ln(x)-(x^3)/9)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 6x^2ln(x)

\int 6 x^{2} ln (x) d x

6 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

Solution steps

\int 6 x^{2} ln (x) d x

Take the constant out:

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

= 6 \cdot \int x^{2} ln (x) d x

Apply Integration By Parts

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

= 6 (\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}

= 6 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9})

Add a constant to the solution

= 6 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

\int \frac{1}{9 x ^{2} - 4} d x

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

e^{- x^{3}}

\int \frac{x}{u}

\int y - x

What is the integral of 6x^2ln(x) ?
The integral of 6x^2ln(x) is 6(1/3 x^3ln(x)-(x^3)/9)+C