What is the integral of xln(x^3) ?

The integral of xln(x^3) is 3/2 x^2ln(x)-(3x^2)/4+C

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integral of xln(x^3)

\int x ln (x^{3}) d x

\frac{3}{2} x^{2} ln (x) - \frac{3 x ^{2}}{4} + C

Solution steps

\int x ln (x^{3}) d x

Apply Integration By Parts

= \frac{1}{2} x^{2} ln (x^{3}) - \int \frac{3 x}{2} d x

\int \frac{3 x}{2} d x = \frac{3 x ^{2}}{4}

= \frac{1}{2} x^{2} ln (x^{3}) - \frac{3 x ^{2}}{4}

\frac{1}{2} x^{2} ln (x^{3}) = \frac{3}{2} x^{2} ln (x)

= \frac{3}{2} x^{2} ln (x) - \frac{3 x ^{2}}{4}

Add a constant to the solution

= \frac{3}{2} x^{2} ln (x) - \frac{3 x ^{2}}{4} + C

\frac{\partial}{\partial x} (\frac{2 x - y}{x + 4 y})

d er i v a t i v e (x - 3)^{- 2}

\frac{d y}{d x} = \frac{e ^{x}}{y ^{2}}

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

\int tan^{6} (x) d x

What is the integral of xln(x^3) ?
The integral of xln(x^3) is 3/2 x^2ln(x)-(3x^2)/4+C