int(4x^(5)-7x^(4)+8x^(3)-2x^(2)+4x-7)/(x^(2)(x^(2)+1)^(2))dx

int(x^(4)-2x^(2)+4x+1)/(x^(3)-x^(2)-x+1)dx

((6x^(4)+8x^(3)+27x^(2)+7)/(3x^(2)+4x+1))

int(2x^(4)+7x^(3)+6x^(2))/(x^(2)+2x)dx

int (5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx=

int(2x+7)/((x+1)(x^(2)+4))dx

Evaluate: (i) int(5x^(2) + 2x^(-5) - 7x + 1/(sqrt(x)) +5/x) dx (ii) int(3sinx - 4 cosx + 5 sec^(2) x - 2cosec^(2)x) dx (iii) int(1-x)(2+3x)(5-4x)dx (iv) int((3x^(4) - 5x^(3) + 4x^(2) -x + 2)/(x^(3)))dx , (v) int(x^(2) + 1/(x^(2)))^(3) dx

int(x^(2)+4x+4)/((x^(2)+5x+7)sqrt(x+2))dx

Find the quotient and remainder of the following using synthetic division: (i) (x^(3) +x^(2) -7x-3) +(x-3) (ii) (x^(3) +2x^(2) -x-4) +(x+2) (iii) (3x^(3) -2x^(2) +7x -5) +(x+3) (iv) (8x^(4) -2x^(2) +6x +5) +(4x+1)

int(x^(6)+7x^(5)+6x^(4)+5x^(3)+4x^(2)+3x+1)e^(x)dx=.......+c

int(x^(6)+7x^(5)+6x^(4)+5x^(3)+4x^(2)+3x+1)e^(x)dx equals