What is the integral from 1 to 4 of x^3ln(x) ?

The integral from 1 to 4 of x^3ln(x) is 128ln(2)-255/16

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 1 to 4 of x^3ln(x)

\int_{1}^{4} x^{3} ln (x) d x

128 ln (2) - \frac{255}{16}

Decimal

72.78533 \dots

Solution steps

\int_{1}^{4} x^{3} ln (x) d x

Apply Integration By Parts

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

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

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

Compute the boundaries:

128 ln (2) - \frac{255}{16}

= 128 ln (2) - \frac{255}{16}

What is the integral from 1 to 4 of x^3ln(x) ?
The integral from 1 to 4 of x^3ln(x) is 128ln(2)-255/16