`int_0^oo x^2/(3x^2 ) dx`

If P=int_0^oo(x^2)/(1+x^4)dx ; Q=int_0^oo(x dx)/(1+x^4)"and"R=int_0^oo(dx)/(1+x^4), then prove that :

int_0^1 x^2(1-x)^(3/2) dx=

int_0^oo (dx)/((x^2+4)(x^2+9)

The value of int_o^oo int_0^oo e^(-(x^2+y^2)) dx

If int_(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int_(0)^(oo) e^(-ax^(2)) dx, a gt0 , s

int_0^3 (3x+1)/(x^2+9) dx=

int_-1^1 (sinx+x^2)/(3-|x|)dx= (A) 0 (B) 2int_0^1 sinx/(3-|x|)dx (C) 2int_0^1 x^2/(3-|x|)dx (D) 2int_0^1 (sinx+x^2)/(3-|x|)dx

int_(0)^(oo)(sin^(2)x)/(x^(2))dx must be same as int_(0)^(oo)(sin x)/(x)dx (b) (int_(0)^(oo)(sin x)/(x))^(2)int_(0)^(2)(cos^(2)x)/(x^(2))(d) none of these

int_(0)^(oo)e^(-x/2)dx

int_(0)^(oo)e^(-x/2)dx