What is the integral from 1 to 2 of x^{11}ln(x) ?

The integral from 1 to 2 of x^{11}ln(x) is -455/16+1024/3 ln(2)

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integral from 1 to 2 of x^{11}ln(x)

\int_{1}^{2} x^{11} ln (x) d x

- \frac{455}{16} + \frac{1024}{3} ln (2)

Decimal

208.15673 \dots

Solution steps

\int_{1}^{2} x^{11} ln (x) d x

Apply Integration By Parts

: [\frac{1}{12} x^{12} ln (x) - \int \frac{x ^{11}}{12} d x]_{1}^{2}

= [\frac{1}{12} x^{12} ln (x) - \int \frac{x ^{11}}{12} d x]_{1}^{2}

\int \frac{x ^{11}}{12} d x = \frac{x ^{12}}{144}

= [\frac{1}{12} x^{12} ln (x) - \frac{x ^{12}}{144}]_{1}^{2}

Compute the boundaries:

- \frac{455}{16} + \frac{1024}{3} ln (2)

= - \frac{455}{16} + \frac{1024}{3} ln (2)

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What is the integral from 1 to 2 of x^{11}ln(x) ?
The integral from 1 to 2 of x^{11}ln(x) is -455/16+1024/3 ln(2)