Tentukanlah Integral Tak Tentu berikut dengan Integral Parsial ∫√x In x dx =

[tex]\displaystyle \int\sqrt x\ln x\,dx=\int\ln x\sqrt x\,dx\\\int\sqrt x\ln x\,dx=\ln x\cdot\frac23x^{\frac32}-\int\frac23x^\frac32\cdot\frac1x\,dx\\\int\sqrt x\ln x\,dx=\frac23x^{\frac32}\ln x-\int\frac23x^\frac12\,dx\\\int\sqrt x\ln x\,dx=\frac23x^{\frac32}\ln x-\frac23\cdot\frac23x^\frac32+C\\\boxed{\boxed{\int\sqrt x\ln x\,dx=\frac29x^{\frac32}(3\ln x-2)+C}}[/tex]