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

= \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

\int \frac{- 2 z - 3}{25 ( z ^{2} + 4 )} d z

y^{^{'}} + 2 y = 5 y^{3}

y^{^{''}} - 2 y^{^{'}} + y = 2 x e^{2 x} + 6 e^{x}

e^{s i n (x)}

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

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