∫1/(x(a+X^n)dx(a为常数,n>0)=?
问题描述：
∫1/(x(a+X^n)dx(a为常数,n>0)=?
答
1/(x(a+x^n))=x^(n-1)/((x^n)(a+x^n))=ax^(n-1)(1/x^n-1/(a+x^n)
∫1/(x(a+X^n)dx=a∫x^(n-1)(1/x^n-1/(a+x^n)dx=a/n∫(1/x^n-1/(a+x^n)d(x^n)
=a/n(nlnx-ln(a+x^n)