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

The integral of x^2*ln(6x) is 1/3 x^3ln(6x)-(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 x^2*ln(6x)

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

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

Solution steps

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

Apply Integration By Parts

: \frac{1}{3} x^{3} ln (6 x) - \int \frac{x ^{2}}{3} d x

= \frac{1}{3} x^{3} ln (6 x) - \int \frac{x ^{2}}{3} d x

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

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

Add a constant to the solution

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

\frac{d}{d x} ((8 x + 15)^{12} (x^{3} + 7)^{13})

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

\frac{d y}{3 x + e ^{x}} = e^{- y} d x

csc (x) (x + cot (x))

x^{7} e^{x}

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