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# Using the integration by parts method, calculate the integral of [x².ln$1/x$]dx: x 4 /4 x³/6 x 4 /8 x³/3 x 4 /6

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## Answer to a math question Using the integration by parts method, calculate the integral of [x².ln$1/x$]dx: x 4 /4 x³/6 x 4 /8 x³/3 x 4 /6

Andrea
4.5
$\int{ {x}^{2} \times \ln\left${{x}^{-1}}\right$ } \mathrm{d} x$
$\int{ {x}^{2} \times \left$-\ln\left({x}\right$ \right) } \mathrm{d} x$
$\int{ -{x}^{2} \times \ln\left${x}\right$ } \mathrm{d} x$
$-\int{ {x}^{2} \times \ln\left${x}\right$ } \mathrm{d} x$
$-\int{ \ln\left${x}\right$ \times {x}^{2} } \mathrm{d} x$
$-\left$\ln\left({x}\right$ \times \frac{ {x}^{3} }{ 3 }-\int{ \frac{ {x}^{3} }{ 3 } \times \frac{ 1 }{ x } } \mathrm{d} x \right)$
$-\left$\ln\left({x}\right$ \times \frac{ {x}^{3} }{ 3 }-\int{ \frac{ {x}^{2} }{ 3 } } \mathrm{d} x \right)$
$-\left$\ln\left({x}\right$ \times \frac{ {x}^{3} }{ 3 }-\frac{ 1 }{ 3 } \times \int{ {x}^{2} } \mathrm{d} x \right)$
$-\left$\ln\left({x}\right$ \times \frac{ {x}^{3} }{ 3 }-\frac{ 1 }{ 3 } \times \frac{ {x}^{3} }{ 3 } \right)$
$-\frac{ \ln\left${x}\right$ \times {x}^{3} }{ 3 }+\frac{ {x}^{3} }{ 9 }$
$\begin{array} { l }-\frac{ \ln\left${x}\right$ \times {x}^{3} }{ 3 }+\frac{ {x}^{3} }{ 9 }+C,& C \in ℝ\end{array}$

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