Prove that `int_(0)^(1)log((1)/(x)-1)dx=0`.

int_(0)^(1)x(1-x)^(n)dx

Evaluate int_(0)^(1)(1)/(3+4x)d x

Prove the following int_(0)^(1)xe^(x)dx=1

Prove that int_(0)^(pi)(x)/(1-cosalphasinx)dx=(pi(pi-alpha))/(sinalpha)

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(1)(2x)/(5x^(2)+1)dx=..........

Using the principle of mathematical induction to prove that int_(0)^(pi//2)(sin^2nx)/(sinx)dx=1+(1)/(3)+(1)/(5)+.....+(1)/(2n-1)

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

Evaluate the definite integrals int_(0)^(1)(2x+3)/(5x^(2)+1)dx

Evaluate the following integrals : int_(0)^(1)(1-x)/(1+x)dx

Find the value of int_(0)^(1)(e^(-x))/(1+e^(x))dx .