Evaluate the integrals `int0 1sin^(-1)((2x)/(1+x^2))dx`

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

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

Evaluate the definite integrals int_0^1 (dx)/(1-x^2)

Evaluate: int_0^1sin^(-1)((2x)/(1+x^2))dx

Evaluate: int_0^1sin^(-1)((2x)/(1+x^2))dx

Evaluate the following integral: int_0^1(2x)/(1+x^4)dx

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

Evaluate the definite integrals int_0^1(2x+3)/(5x^2+1)dx

Evaluate: int_0^(1)sin^(-1)((2x)/(1+x^2))dx