Question

求助一道不定积分的题目

主要是算到(x^3)/3+∫lnxd【(2x^3）/3】这步后∫lnxd【(2x^3）/3】如何向下解：希望知道的朋友解答下

Answer 1

F(x)=∫f(x) dx=x²lnx
f(x)=(x²lnx)'
=lnx*2x + x²*1/x
=2xlnx + x
∫xf(x) dx
=∫x(2xlnx + x) dx
=∫(x² + 2x²lnx) dx
=x³/3 + 2∫x²lnx dx
=x³/3 + 2∫lnx d(x³/3)
=x³/3 + 2[(x³/3)lnx - (1/3)∫x³ d(lnx)]
=x³/3 + (2/3)x³lnx - (2/3)∫x² dx
=x³/3 + (2/3)x³lnx - (2/3)(x³/3) + C
=x³/3 + (2/3)x³lnx - (2/9)x³ + C