Question

求一道微积分

Answer 1

见下图：

Answer 2

如下图所示，用分部积分法做
∫xlnxdx
=∫lnxd(x^2/2)
=x^2lnx/2-∫(x/2）dx
=x^2lnx/2-x^2/4+C
=x^2*(2lnx-1)/4+C

Answer 3

∫ xlnx dx
=(1/2)∫ lnx dx^2
=(1/2)x^2.lnx - (1/2)∫ x dx
=(1/2)x^2.lnx - (1/4)x^2 +C

Answer 4

∫xlnxdx=½∫lnxdx²=½x²lnx-½∫xdx=½x²lnx-¼x²+C

Answer 5

∫xlnxdx=(1/2)∫lnxd(x²)=(1/2)[x²lnx-∫x²d(lnx)]
=(1/2)[x²lnx-∫xdx]=(1/2)[x²lnx-(1/2)x²]+C
=(1/2)x²[lnx-(1/2)]+C