int_(0)^(1)(x ln x)^(4)dx

Let I_(n)= int_(0)^(1)(x ln x)^(n)dx, if I_(4)=k int_(0)^(1)x^(4)(ln x)^(3)dx, then |[k]| is equal to ([.] denotes greatest integer function).

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

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

Evaluate int_(5)^(7)ln(x-3)^(2)dx+2int_(0)^(1)ln(x+4)^(2)dx

Evaluate int _(0) ^(1) ln x dx.

(int_(0)^(1)ln x ln(1-x)dx)/(int_(0)^((1)/(sqrt(2)))x ln x ln(1-x^(2))dx) is equal to

int_(0)^(1)ln(1+x^(2))*dx

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

Show that :int_(0)^(1)(log x)/((1+x))dx=-int_(0)^(1)(log(1+x))/(x)dx

Evaluate int_(0)^(1)(ln(1+x))/(1+x)dx