计算曲线y=lnx在√3≤x≥√8上的一段弧长.(不用积分表)

1)
(x+y)^4(x-y)^4
=[(x+y)(x-y)]^4
=(x^2-y^2)^4
=[(x^2-y^2)^2]^2
=
(x^4-2x^2y^2+y^4)^2
=x^8+4x^4y^4+y^8-4x^6y^2+2x^4y^4-4x^2y^6;
(2)
(a+3b)(a^2-3ab+9b^2)-(a-3b)(a^2+3ab+9b^2)
=(a^3+27b^3)-(a^3-27b^3)
=54b^3；
(3)(x+y)^2(y+z-x)(z+x-y)+(x-y)^2(x+y+z)*(x+y-z)
=(x+y)^2*[z^2-(x-y)^2]+(x-y)^2*[(x+y)^2-z^2]
=(x+y)^2z^2-(x+y)^2(x-y)^2+(x-y)^2(x+y)^2-(x-y)^2z^2
=(xz+yz)^2-(xz-yz)^2
=x^2z^2+2xyz^2+y^2z^2-x^2z^2+2xyz^2-y^2z^2
=4xyz^2;
4．因为(x^2-2x+3)*(2x+7)+7x-19=f(x)=2x^3+3x^2-x+2，
f(x)/(x2-2x+3)所得的商式为2x+7.

不用积分好像算不了