What is the integral from 0 to 1 of xln(x^2) ?

The integral from 0 to 1 of xln(x^2) is -1/2

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integral from 0 to 1 of xln(x^2)

\int_{0}^{1} x ln (x^{2}) d x

- \frac{1}{2}

Decimal

- 0.5

Solution steps

\int_{0}^{1} x ln (x^{2}) d x

Apply Integration By Parts

= [\frac{1}{2} x^{2} ln (x^{2}) - \int x d x]_{0}^{1}

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

= [\frac{1}{2} x^{2} ln (x^{2}) - \frac{x ^{2}}{2}]_{0}^{1}

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

= [x^{2} ln (x) - \frac{x ^{2}}{2}]_{0}^{1}

Compute the boundaries:

- \frac{1}{2}

= - \frac{1}{2}

What is the integral from 0 to 1 of xln(x^2) ?
The integral from 0 to 1 of xln(x^2) is -1/2