What is the integral of xln(x^5) ?

The integral of xln(x^5) is 5/2 x^2ln(x)-(5x^2)/4+C

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integral of xln(x^5)

\int x ln (x^{5}) d x

\frac{5}{2} x^{2} ln (x) - \frac{5 x ^{2}}{4} + C

Solution steps

\int x ln (x^{5}) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (x^{5}) - \int \frac{5 x}{2} d x

= \frac{1}{2} x^{2} ln (x^{5}) - \int \frac{5 x}{2} d x

\int \frac{5 x}{2} d x = \frac{5 x ^{2}}{4}

= \frac{1}{2} x^{2} ln (x^{5}) - \frac{5 x ^{2}}{4}

\frac{1}{2} x^{2} ln (x^{5}) = \frac{5}{2} x^{2} ln (x)

= \frac{5}{2} x^{2} ln (x) - \frac{5 x ^{2}}{4}

Add a constant to the solution

= \frac{5}{2} x^{2} ln (x) - \frac{5 x ^{2}}{4} + C

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What is the integral of xln(x^5) ?
The integral of xln(x^5) is 5/2 x^2ln(x)-(5x^2)/4+C