If `I_m=int_1^x(logx)^mdx` satisfies the relation `(I_m)=k-l I_(m-1) then`

Given I_m=int_1^e(logx)^mdx ,then prove that (I_m)/(1-m)+m I_(m-2)=e

I=int 1/x logx dx =

If I_m=int_1^e (lnx)^m dx ,m in N , then I_(10)+10 I_9 is equal to (A) e^(10) (B) (e^(10))/(10) (C) e (D) e-1

If I=int_(3)^(4) (1)/(3sqrt(logx))dx then

If I(m,n)=int_0^1x^(m-1)(1-x)^(n-1)dx , then

If I(m,n)=int_0^1 t^m(1+t)^n.dt , then the expression for I(m,n) in terms of I(m+1,n-1) is:

IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx , Then show that I_(m , n)=(m-1)/(m+n)I_(m-2,n)(m ,n in N) Hence, prove that I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4 when both m and n are even ((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))}

int (x^2)/(x^2+1)+x^mdx

Let I_m=int_0^pi (1-cosmx)/(1-cosx)dx . Show that I_m=mpi .

If I_(m,n)= int(sinx)^(m)(cosx)^(n) dx then prove that I_(m,n) = ((sinx)^(m+1)(cosx)^(n-1))/(m+n) +(n-1)/(m+n). I_(m,n-2)