What is the integral from 1 to 2 of 4x^2ln(x) ?

The integral from 1 to 2 of 4x^2ln(x) is 4(-7/9+8/3 ln(2))

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integral from 1 to 2 of 4x^2ln(x)

\int_{1}^{2} 4 x^{2} ln (x) d x

4 (- \frac{7}{9} + \frac{8}{3} ln (2))

Solution steps

\int_{1}^{2} 4 x^{2} ln (x) d x

Take the constant out:

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

= 4 \cdot \int_{1}^{2} x^{2} ln (x) d x

Apply Integration By Parts

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

= 4 [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{1}^{2}

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= 4 [\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}]_{1}^{2}

Compute the boundaries:

- \frac{7}{9} + \frac{8}{3} ln (2)

= 4 (- \frac{7}{9} + \frac{8}{3} ln (2))

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\int_{0}^{1} \frac{28}{x ^{2} - 49} d x

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What is the integral from 1 to 2 of 4x^2ln(x) ?
The integral from 1 to 2 of 4x^2ln(x) is 4(-7/9+8/3 ln(2))