Evaluate: `int(log_(e x)e*log_(e^2x)e*log_(e^3x)e)/x dx`

Evaluate int log_e(a^x)dx

Evaluate int(log_(e)x)^(2)dx

int2^(log_(e)x)dx

I=int(log_(e)(log_(e)x))/(x(log_(e)x))dx

int e^(log_(e)x)dx

Evaluate: int e^(log_(e)(x^(2))log_(e)x)xdx

Evaluate int e^x/log(e^x)dx

Evaluate int(1+x^(2)log_(e)x)/(x+x^(2)log_(e)x)dx

If int(log_(x)e.log_(ex)e.log_(e^(2)x)e)/(x)dx=A log_(e)(log_(e)x)+Blog_(e)(1+log_(e)x)+Clog_(e)(2+log_(e)x)+lambda, then