`int_0^1(dx)/(1+x+x^2)`

int_0^1(dx)/(1-x^2)\

(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

If int_0^1 (dx)/(sqrt(1 + x) - sqrt(x)) =(ksqrt(2))/(3) , then k is :

Show that int_(0)^(1)(dx)/((1+x^(2))sqrt(2+x^(2))) = (pi)/(6)

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_0^1log(1+x)/(1+x^2)dx

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

The value of int_0^oo (dx)/(1+x^4) is (a) same as that of int_0^oo (x^2+1dx)/(1+x) (b) (pi)/(2sqrt2) (c) same as that of int_0^oo (x^2+1dx)/(1+x^4) (d) pi/sqrt2

Evaluate int_0^1 x/(1+x^2) dx

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