What is the integral of ln(x)x^3 ?

The integral of ln(x)x^3 is 1/4 x^4ln(x)-(x^4)/(16)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of ln(x)x^3

\int ln (x) x^{3} d x

\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16} + C

Solution steps

\int ln (x) x^{3} d x

Apply Integration By Parts

= \frac{1}{4} x^{4} ln (x) - \int \frac{x ^{3}}{4} d x

\int \frac{x ^{3}}{4} d x = \frac{x ^{4}}{16}

= \frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}

Add a constant to the solution

= \frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16} + C

What is the integral of ln(x)x^3 ?
The integral of ln(x)x^3 is 1/4 x^4ln(x)-(x^4)/(16)+C