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

The integral of (ln(x))x^2 is 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 (ln(x))x^2

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

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

Solution steps

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

Apply Integration By Parts

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

= \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}

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

Add a constant to the solution

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

x \to \frac{1}{2} lim (x^{3} - x^{2} - x + 1)

\int_{0}^{3} x^{2} - 4 d x

f (t) = 3 cos (2 t)

n = 0 \sum \infty 3^{- n}

x \to - 4 - lim (\frac{- 5 x}{x + 4})

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