Question

高数有理函数积分题∫(x^5+x^4-8)/(x^3-x)dx 求详细过程,多谢啊1L：求详细过程,没过程不给分！谢谢

Answer 1

(x^5+x^4-8)(x^3-x)

=(x^5-x^3+x^3-x+x^4-x^2+x^2+x-8)x(x+1)(x-1)

=x^2+x+1+(x^2+x-8)x(x-1)(x+1)

设(x^2+x-8)x(x-1)(x+1)=ax+b(x-1)+c(x+1)

a+b+c=1 -a=-8 b-c=1

a=8 b=-3 c=-4

∴∫(x^5+x^4-8)/(x^3-x)dx

=x^33+x^22+x+8In|x|-3In|x-1|-4In|x+1|+C