And dr = dt - + C (16) Where C1 + C2 = C 2x +1 Find the integral of x with respect to x. 2x2 + x -3 (2012) questions 3.

If the value of integral int(x+sqrt(x^2 -1))^(2)dx = ax^3 - x + b(x^2 - 1)^(1/b), +C (where, C is the constant of integration), then a xx b is equal to

If the value of integral int(x+sqrt(x^2 -1))^(2)dx = ax^3 - x + b(x^2 - 1)^(1/b), +C (where, C is the constant of integration), then a xx b is equal to

If int(dx)/((x+1)^(2)(x^(2)+2x+2))=(A)/(x+1)+B tan^(-1)(x+1)+C, where A and B are constants and C is the constant of integration, then |A-B| is equal to

If int(dx)/((x+1)^(2)(x^(2)+2x+2))=(A)/(x+1)+B tan^(-1)(x+1)+C, where A and B are constants and C is the constant of integration, then |A-B| is equal to

If the integral I=int(x^(5))/(sqrt(1+x^(3)))dx =Ksqrt(x^(3)+1)(x^(3)-2)+C , (where, C is the constant of integration), then the value of 9K is equal to

If the integral I=int(x^(5))/(sqrt(1+x^(3)))dx =Ksqrt(x^(3)+1)(x^(3)-2)+C , (where, C is the constant of integration), then the value of 9K is equal to

If (1 + x + x^2)^n = C_0 + C_1x + C_2x^2 + C_3x^3 + ……..C_nx^n then find C_0 + C_3 + C_6 + …….

If (1 + x + x^2)^n = C_0 + C_1x + C_2x^2 + C_3x^3 + ……..C_nx^n then find C_0 + C_3 + C_6 + …….

If int(dx)/((x^(2)+x+1)^(2))=atan^(-1)((2x+1)/(sqrt(3)))+b((2x+1)/(x^(2)+x+1))+C , x gt 0 where C is the constant of integration, then the value of 9(sqrt(3)a+b) is equal to __________.

If the integral I=inte^(x^(2))x^(3)dx=e^(x^(2))f(x)+c , where c is the constant of integration and f(1)=0 , then the value of f(2) is equal to