`int x log (1+x^2)dx`

overset(1)underset(0)int x log(1+2x)dx

Evaluate the following (i) int x log (1+x) dx (ii) int x log^2x dx

int 1/(x(log x)^2)dx

int(x log(x+1)^(2)dx)

If int_0^1 x log(1+x/2) \ dx=a+b log\ 2/3, then a and b are

Evaluate int x^(2)log (1-x^(2))dx , and hence prove that (1)/(1.5)+(1)/(2.7)+(1)/(3.9)+...=2/3 log 2 - 8/9 .

Evaluate int x^(2)log (1-x^(2))dx , and hence prove that (1)/(1.5)+(1)/(2.7)+(1)/(3.9)+...=2/3 log 2 - 8/9 .

If a=lim_(x->oo) sinx/x & b=lim_(x->0) sinx/x Then int (ab log(1+x)+x^2)dx is equal to

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