Question #4fa34

1 Answer
Pankaj Solanki
Oct 1, 2017

Just Divide #x^2# by (x-1) Using division Algorithm
we get #x^2/(x-1)=x+1+1/(x-1)#
1 in last term is remainder
and
#int(x^2/(x-1))dx=int(x+1+1/(x-1))dx#
#=x^2/2+x+log(x-1)+c#

OR

#intx^2/(x-1)dx=int(x^2-2x+1+2x-1)/(x-1)dx#
#=int((x-1)^2+2x-1)/(x-1)dx#
#=int((x-1)^2/(x-1)+(2x-1)/(x-1))dx#
#=int((x-1)+(x+x-1)/(x-1))dx#
#=int((x-1)+1+(x)/(x-1))dx#
#=int((x-1)+1+(x+1-1)/(x-1))dx#
#=int((x-1)+1+1+1/(x-1))dx#
#=int((x-1)+2+1/(x-1))dx#
#=x^2/2-x+2x+log(x-1)+c#
#=x^2/2+x+log(x-1)+c#

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