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

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

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

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

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

Evaluate: underset0oversetinfty int 1/(1+x^2)log (x+1/x)dx

1) int x log x^(2)dx

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