`int_(0)^(1)x log (1+2 x)dx`

Evaluate :int_(0)^(1)x log(1+2x)dx

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

Evaluate the following definite integrals: int_(0)^(1)x log(1+x/2)dx

Which of the following is true Statement-I : int_(0)^(2pi) sqrt((1-cos2x)/(2)) dx=4 Statement-II : int_(-1)^(1) log((1+x)/(1-x))dx= 2 int_(0)^(1) log (1+ x)/(1-x)dx

int_(0)^(1)(1+x)*log(1+x)dx=

int_(0)^(1)(log x)dx

int_(0)^(1)(log(1-x))/(x)dx

int_(1)^(2)x log x dx =

int_(1)^(2)x log x dx =