设分母√x=t
则
x=t^2
dx=2tdt
则原式化为
∫(1-t^2)^2*2tdt/t
=2∫(1-t^2)^2dt
=2∫(1-2t^2+t^4)dt
=2t-4t^3/3+2t^5/5+C
=2√x-4√x^3 / 3 +2√x^5 / 5 +C
=2√x-4x√x /3+2x^2√x / 5 +C
设分母√x=t
则
x=t^2
dx=2tdt
则原式化为
∫(1-t^2)^2*2tdt/t
=2∫(1-t^2)^2dt
=2∫(1-2t^2+t^4)dt
=2t-4t^3/3+2t^5/5+C
=2√x-4√x^3 / 3 +2√x^5 / 5 +C
=2√x-4x√x /3+2x^2√x / 5 +C