Selesaikan integral berikut: integral x^2 ln (x^2) dx

[tex]\displaystyle \int x^2\ln x^2 \,dx=\int2x^2\ln x\,dx\\\int x^2\ln x^2 \,dx=\frac23x^3\ln x-\int\frac23x^3\cdot\frac1x\,dx\\\int x^2\ln x^2 \,dx=\frac23x^3\ln x-\int\frac23x^2\,dx\\\int x^2\ln x^2 \,dx=\frac23x^3\ln x-\frac29x^3\\\boxed{\boxed{\int x^2\ln x^2 \,dx=\frac29x^3(3\ln x-1)}}[/tex]