Evaluate : `int_0^1xlog(1+2x)dx`

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

Evaluate: int_0^1log(x^2+x+1)dx

Evaluate int_(0)^(1) xlog(1+x)dx and hence show that, (1)/(1xx3)-(1)/(2xx4)+(1)/(3xx5)-(1)/(4xx6)+..=(1)/(4)

Integrate: int_0^1 xlog(1+x)dx

Evaluate : int_0^1 1/(1+x^2)dx

Evaluate: int_0^pi x/(1+cos^2x)dx

Evaluate: int_0^1 xsqrt(1+x^2) dx

Evaluate: int2^(xlog_(2)^(3)) dx

Evaluate: int2^(xlog_(2)^(3)) dx

Evaluate int_0^1 x/(1+x^2) dx