Prove that `int_0^1 tan^-1((2x-1)/(1+x-x^2))dx=0`

Prove that int_0^1tan^(-1)(1/(1-x+x^2))dx=2int_0^1tan^(-1)x dx . Hence or otherwise, evaluate the integral int_0^1tan^(-1)(1-x+x^2)dx

Prove that int_0^1tan^(-1)(1/(1-x+x^2))dx=2int_0^1tan^(-1)x dxdot Hence or otherwise, evaluate the integral int_0^1tan^(-1)(1-x+x^2)dx

STATEMENT 1 : The value of int_0^1tan^(-1)((2x-1)/(1+x-x^2)) dx=0 STATEMENT 2 : int_a^bf(x)dx=int_0^bf(a+b-x)dx then Which of the following statement is correct ?

Prove that int_0^1x e^x dx=1

Evaluate the following integral: int_0^1tan^(-1)((2x)/(1-x^2))dx

The value of int_(0)^(1) tan^(-1)((2x-1)/(1+x-x^(2)))dx is

The value of int_0^1tan^(-1)((2x-1)/(1+x-x^2))dx ,\ is a. 1 b. -1 c. 0 d. pi//4

Evaluate the following integral: int_0^1tan^(-1)\ ((2x)/(1-x^2))dx

2) int_(0)^(1)tan^(-1)(1-x+x^(2))dx

int_0^1 x^5sqrt((1+x^2)/(1-x^2))dx