求不定积分fx3Inxdx（x3为x的3次方）~
问题描述：
求不定积分fx3Inxdx（x3为x的3次方）~
答
构造一个函数：g(x) = x^4*lnx
g'(x) = 4*x^3*lnx + x^3 = 4*f(x) + x^3
f(x) = g'(x)/4 - (x^3)/4
∫[f(x)*dx]
= g(x)/4 - [∫x^3*dx]/4 + C
= (x^4*lnx)/4 - (x^4)/16 + C
= x^4*(4*lnx - 1)/16 + C