`int(a x^2+b x+c)dx`

Evaluate: (i) int{sqrt(x)(a x^2+b x+c)}\ dx (ii) int(2-3x)(3+2x)(1-2x)\ dx

int(ax^(2)+bx+c)/((x-a)(x-b)(x-c))dx;a,b,c are distinct

Which of the following is incorrect? int_(a+c)^(b+c)f(x)dx=int_(a)^(b)f(x+c)dxint_(a+c)^(bc)f(x)dx=c int_(a)^(b)f(cx)dxint_(-ac)^(a)f(x)dx=(1)/(2)int_(-a)^(a)(f(x)+f(-x)dx None of these

Prove that int_(a)^(b) f(x)dx=int_(a)^(c)f(x)dx+int_(c)^(b)f(x)dx

If f(a+b-x)=f(x) , then int_a^b x f(x)dx is equal to (A) (a-b)/2int_a^b f(a+b-x)dx (B) (a+b)/2int_a^b f(b-x)dx (C) (a+b)/2int_a^b f(x)dx (D) (b-a)/2int_a^b f(x)dx

Evaluate: int_(-pi/2)^(pi/2)log{(a x^2+b x+c)/(a x^2-b x+c)(a+b)|sinx|}dx

Evaluate: int_(-pi/2)^(pi/2)log{(a x^2+b x+c)/(a x^2-b x+c)(a+b)|sinx|}dx

Evaluate: int_(-pi/2)^(pi/2)log{(a x^2+b x+c)/(a x^2-b x+c)(a+b)|sinx|}dx

Evaluate: int_(-pi/2)^(pi/2)log{(a x^2+b x+c)/(a x^2-b x+c)(a+b)|sinx|}dx

Integrate the following functions with respect to x (a) int (5x^2 + 3x -2) dx (b) int (4sin x-(2)/(x)) dx (c) int (dx)/(4x+5) (d) int (6x +2)^(3) dx