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

"int x^(n)(log x)^(2)dx

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 .

Evaluate int x^(2) log x dx

int(log x)^(2)dx=

int x (log x)^(2)dx