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

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

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

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

Assertion (A) : int(dx)/(x^(2) + 2x + 3) = (1)/(sqrt(2)) tan^(-1)((x+1)/(sqrt(2))) + c Reason (R) : int(dx)/(x^(2) + a^(2)) = (1)/(a) tan^(-1)((x)/(a)) + c

int (dx)/((x+1)(2x+1)) (ii) int (x-1)/((x-2)(x-3)) dx .

(i) int_0^1 (dx)/sqrt(1-x^2) (ii) int_0^1 (dx)/sqrt(1+x^2) (iii) a int_1^sqrt3 (dx)/(1+x^2) b int_0^1 (dx)/(1+x^2) (iv) int_0^(2//3) (dx)/(4+9x^2) (v) int_0^1 x/(x^2+1)dx (vi) int_2^3 x/(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))

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