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

By using the properties of definite integrals, evaluate the integrals int_0^1x(1-x)^n dx

Evaluate the integrals int_(0)^(1)(x)/(x^(2)+1)dx

By using the properties of definite integrals, evaluate the integral: int_0^1 x(1-x)^n dx

evaluate the integrals int_(0)^(1)x(1-x)dx

Evaluate the integrals . I=int_(0)^(1) (x^(2))/(x^(2)+1)dx

Evaluate the integral int_(0)^(1) x^(7//2)(1-x)^(5//2) dx

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

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

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