hiiiiiii megha

 

Let me try to solve this one ...

 

first of all let me tell u it is 2x^2m + 3x^m + 6 rather than 2x^2m + 3x^m + 6x^m in the question .... if this was printed wrong in the question displayed on the website yesterday then I seriously apologise

 

well now, let us see how we can start .. try to observe the coefficients 2,3, and 6 in the expression 2x^2m + 3x^m + 6

 

These give us some indication ... let us see what

 

well we will do some manipulation now

 

I = (x^3m + x^2m + x^m) (2x^2m + 3x^m + 6)^1/mdx

  = (x^3m + x^2m + x^m) [(2x^3m + 3x^2m + 6x^m)^1/m]/x dx

  = (x^3m-1 + x^2m-1 + x^m-1) (2x^3m + 3x^2m + 6x^m)^1/m dx    

 

Now let us put 2x^3m + 3x^2m + 6x^m = p

 

so, 6m.(x^3m-1 + x^2m-1 + x^m-1)dx = dp

 

Thus, now I = p^1/m dp/6m 

                 = 1/6m.(p^{1/m + 1})/(1/m+1) + c  

 

Now puttin back p = 2x^3m + 3x^2m + 6x^m

 

so, we get I = 1/(6(m+1)).[ 2x^3m + 3x^2m + 6x^m]^m+1/m + c

 

If the confusion arised out of the misprint .. I am once again sorry

 

cheers