What is the integral of xln(x^4) ?

The integral of xln(x^4) is 2x^2ln(x)-x^2+C

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integral of xln(x^4)

\int x ln (x^{4}) d x

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

Solution steps

\int x ln (x^{4}) d x

Apply Integration By Parts

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

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

= \frac{1}{2} x^{2} ln (x^{4}) - x^{2}

\frac{1}{2} x^{2} ln (x^{4}) = 2 x^{2} ln (x)

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

Add a constant to the solution

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