`int_0^([x])(2^x)/(2^([x]))dx`

If [.] represent greatest integer less than or equal to x, then int_0^2 (x+[x-2[x]])^([2x]) dx=

int_0^2sqrt((2+x)/(2-x))dx=

int_(0)^(2) (2x-2)/(2x-x^(2)) dx is equal to

If A=int_(0)^( pi)(sin x)/(x^(2))dx, then int_(0)^((pi)/(2))(cos(2x))/(x)dx, is equal to:

int_0^2[x^2]dx=?

If int_(0)^(1)f(x)dx=1, int_(0)^(1)x f(x)dx=a and int_(0)^(1)x^(2)f(x)dx=a^(2) , then : int_(0)^(1)(a-x)^(2)f(x)dx=

Let I_1=int_0^1e^(x^2)dx and I_2=int_0^(12)2^(x^2)e^(x^2)dx then the value of I_1 +I_2 is equal to

int_0^1 (x+x^2)dx

int_0^1(x^2)/(1+x^2)dx=?

int_0^2(x^3+2x)dx=?