What is the integral from 1 to 2 of x^2ln(x^3) ?

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

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integral from 1 to 2 of x^2ln(x^3)

\int_{1}^{2} x^{2} ln (x^{3}) d x

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

Decimal Notation

3.21184 \dots

Solution steps

\int_{1}^{2} x^{2} ln (x^{3}) d x

Apply Integration By Parts

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

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

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

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

\frac{1}{3} x^{3} ln (x^{3}) = x^{3} ln (x)

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

Compute the boundaries:

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

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

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