Simone求33、34题解法
的有关信息介绍如下：
(33) ∫ √x/[ √x - x^(1/3) ] dxletu = x^(1/6)du = (1/6)x^(-5/6) dxdx = 6u^5 du∫ √x/[ √x - x^(1/3) ] dx=∫ { u^3/[ u^3 - u^2 ] } ( 6u^5 du )=6∫ { u^6/ (u - 1) du=6∫ [ u^5+u^4+u^3+u^2+u+1 + 1/ (u - 1) ] du=6[ (1/6)u^6 + (1/5)u^5 +(1/4)u^4+(1/3)u^2+ u + ln|u-1| ] + C=6[(1/6)x+(1/5)x^(5/6) +(1/4)x^(2/3)+(1/3)x^(1/3)+ x^(1/6) + ln|x^(1/6)-1|] + C(34)x^2-2x+5=(x-1)^2 +4letx-1 = 2tanudx=2(secu)^2 . du∫dx/ √(5-2x+x^2)=∫2(secu)^2 . du/ [2secu]=∫secu du=ln|secu+ tanu| +C=ln|(1/2)√(5-2x+x^2)+x-1| + C
