What is the integral from 1 to 3 of 17x^3ln(x) ?

The integral from 1 to 3 of 17x^3ln(x) is 17(-5+81/4 ln(3))

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integral from 1 to 3 of 17x^3ln(x)

\int_{1}^{3} 17 x^{3} ln (x) d x

17 (- 5 + \frac{81}{4} ln (3))

Decimal Notation

293.19728 \dots

Solution steps

\int_{1}^{3} 17 x^{3} ln (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 17 \cdot \int_{1}^{3} 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}^{3}

= 17 [\frac{1}{4} x^{4} ln (x) - \int \frac{x ^{3}}{4} d x]_{1}^{3}

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

= 17 [\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}]_{1}^{3}

Compute the boundaries:

- 5 + \frac{81}{4} ln (3)

= 17 (- 5 + \frac{81}{4} ln (3))

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\frac{2}{s ^{2} ( s ^{2} + 3 s + 10 )}

What is the integral from 1 to 3 of 17x^3ln(x) ?
The integral from 1 to 3 of 17x^3ln(x) is 17(-5+81/4 ln(3))