What is the integral from 1 to 3 of x^5ln(x^2) ?

The integral from 1 to 3 of x^5ln(x^2) is 243ln(3)-364/9

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integral from 1 to 3 of x^5ln(x^2)

\int_{1}^{3} x^{5} ln (x^{2}) d x

243 ln (3) - \frac{364}{9}

Decimal

226.51834 \dots

Solution steps

\int_{1}^{3} x^{5} ln (x^{2}) d x

Apply Integration By Parts

: [\frac{1}{6} x^{6} ln (x^{2}) - \int \frac{x ^{5}}{3} d x]_{1}^{3}

= [\frac{1}{6} x^{6} ln (x^{2}) - \int \frac{x ^{5}}{3} d x]_{1}^{3}

\int \frac{x ^{5}}{3} d x = \frac{x ^{6}}{18}

= [\frac{1}{6} x^{6} ln (x^{2}) - \frac{x ^{6}}{18}]_{1}^{3}

\frac{1}{6} x^{6} ln (x^{2}) = \frac{1}{3} x^{6} ln (x)

= [\frac{1}{3} x^{6} ln (x) - \frac{x ^{6}}{18}]_{1}^{3}

Compute the boundaries:

243 ln (3) - \frac{364}{9}

= 243 ln (3) - \frac{364}{9}

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What is the integral from 1 to 3 of x^5ln(x^2) ?
The integral from 1 to 3 of x^5ln(x^2) is 243ln(3)-364/9