令x=1/t,则有： ∫dx/[x(1+x^6)] =∫d(1/t)/[(1/t)[1+(1/t)^6] =-∫t^5dt/(1+t^6) =-(1/6)∫d(t^6)/(1+t^6) =-(1/6)∫d(t^6+1)/(1+t^6) =-(1/6)ln(1+t^6)+c =-(1/6)ln[1+(1/x)^6]+c.
