求不定積分

∫x(lnx)²dx

= (1/2)∫(lnx)²dx²

= (1/2)[(lnx)²x² - ∫x²d(lnx)²]

= (1/2)[x²(lnx)² - ∫x²*2(lnx)*(1/x)dx]

= (1/2)[x²(lnx)² - 2∫x(lnx)dx]

= (1/2)[x²(lnx)² - ∫(lnx)dx²]

= (1/2)[x²(lnx)² - (lnx)x² + ∫x²d(lnx)]

= (1/2)[x²(lnx)² - (lnx)x² + ∫x²(1/x)dx]

= (1/2)[x²(lnx)² - (lnx)x² + ∫xdx]

= (1/2)[x²(lnx)² - (lnx)x² + (x²/2)] + C

= (x²/4)[2(lnx)² - 2(lnx) + 1] + c

∫x(Inx)^2 dx = (x^2/2)(ln(x))^2 - ∫(x^2/2)2(ln(x))(1/x) dx
= x^2(ln(x))^2/2 - ∫x(ln(x)) dx
再做一次分部積分.

你自己都知道要分部積分2次了...