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

The integral from 1 to 4 of x^2ln(x) is -7+128/3 ln(2)

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

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

- 7 + \frac{128}{3} ln (2)

Decimal

22.57427 \dots

Solution steps

\int_{1}^{4} 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}^{4}

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

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

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

Compute the boundaries:

- 7 + \frac{128}{3} ln (2)

= - 7 + \frac{128}{3} ln (2)

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\int_{0}^{\frac{π}{3}} t^{2} sin (3 t) d t

What is the integral from 1 to 4 of x^2ln(x) ?
The integral from 1 to 4 of x^2ln(x) is -7+128/3 ln(2)