`(2x^(3)+3x^(2)-3)/(2x^(2)-x-1)`

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

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

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

The value of: (9^(x)(9^(x-1)))^(x)/(9^(x+1).3^(2x-2)){(729^(x/3))/81}^(-x) + (3^(a) -2^(3) .3^(a-2))/(3^(a) -3^(a-1)) is:

Value of ((x-1)^(3)+(2x-1)^(3)-(3x2)^(3))/((x-1)(2x-1)(3x-2)) is equal to (A)-3(B)0(C)1(D)3

Simplify: (x^(3)-2x^(2)+3x-4)(x-1)-(2x-3)(x^(2)-x+1)

(i) (2x+3) (3x-5) (ii) x(1+x)^(3) (iii) (sqrtx + 1/x) (x -1/sqrtx) (iv) (x-1/x)^(2) (v) (x^(2) + 1/x^(2))^(3) (vi) (2x^(2) +5x-1) (x-3)

lim_(x rarr oo)((3x^(2)+1)/(2x^(2)-1))^((x^(3))/(1-x))

lim_(x rarr oo)((3x^(2)+1)/(2x^(2)-1))^((x^(3))/(1-x))

Find the sum of the following algebraic expressions : 3x^(3) - 5x^(2) + 2x + 1 , 3x - 2x^(3) - x^(3) , 2x^(2) - 7x + 9