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

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

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integral of x(ln(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

\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

ma c l a u r in e^{s i n (x)}

\int (x^{7} - 3 x^{4} + x) d x

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\int 7 cos^{5} (x) sin^{4} (x) d x

x \to a lim (3)

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