If `I_n=int_1^e(log_e x)^n dx` (n is a positive number), `I_2012+(2012)I_2011=`

int_1^(e) x^(n) log x dx

If I_(n)=int_(1)^(e)(ln x)^(n)dx(n is a natural number) then I_(2020)+nI_(m)=e, where n,m in N .The value of m+n is equal to

If I_(n)=int_(1)^(e)(log x)^(n)dx then I_(8)+8I_(7)=

If I_(n)= int_(1)^(e) (log x)^(n) dx then I_(8) + 8I_(7)=

If I=int e^(-x) log(e^x+1) dx, then equal

If I_(n)=int_(1)^(e)(log x)^(n) d x, then I_(n)+nI_(n-1) equal to

If I_(n) = int (log x)^(n) dx then I_(6) + 6I_(5) =

Let I_(n) = int_(0)^(1) (logx)^(n)dx , where n is a non-negative integer. Then I_(2001) - 2011 I_(2010) is equal to -

If I=int e^(-x)log(e^(x)+1)dx, then equal