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

Evaluate : int(x^(2) +1)"log x dx"

Evaluate: int sin^(2)(log x)dx

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

Evaluate : int x log 2x 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^(3)(log x)^(2)dx