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

If int((log_(ex)e)(log_(e^(2)x)e)log_(e^(3)x) e))1/x dx = Alog |1+logx|+B log |2+log x|+C log |3+ logx| +D then A-B+C is equal to

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

The value of int(e^(5log_(e)x)+e^(4log_(e)x))/(e^(3log_(e)x)+e^(2log_(e)x))dx is

I=int \ log_e (log_ex)/(x(log_e x))dx

Evaluate: int_(-log2)^(log2) e^(-|x|) dx.

e ^(x log a)e^(x)

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

Evaluate: int(e^x)/(e^(2x)+6e^x+5)dx

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