What is the integral of xln(x^2) ?

The integral of xln(x^2) is x^2ln(x)-(x^2)/2+C

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integral of xln(x^2)

\int x ln (x^{2}) d x

x^{2} ln (x) - \frac{x ^{2}}{2} + C

Solution steps

\int x ln (x^{2}) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (x^{2}) - \int x d x

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

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

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

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

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

Add a constant to the solution

= x^{2} ln (x) - \frac{x ^{2}}{2} + C

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What is the integral of xln(x^2) ?
The integral of xln(x^2) is x^2ln(x)-(x^2)/2+C