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

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

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

\frac{1}{3} x^{3} ln (2 x) - \frac{x ^{3}}{9} + C

Solution steps

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

Apply Integration By Parts

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

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

Add a constant to the solution

= \frac{1}{3} x^{3} ln (2 x) - \frac{x ^{3}}{9} + C

\frac{d}{d x} (arccos (ln (x)))

\frac{d}{d t} (3 sin (2 t))

\int_{3}^{5} x^{2} d x

\int \frac{t ^{3}}{t ^{3} + 1} d t

\frac{1}{( s ^{2} + 5 s + 4 )}

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