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find ( int( x^n / x+1)dx)  

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user9880347 | eNotes Newbie

Posted February 23, 2013 at 8:38 AM via web

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find ( int( x^n / x+1)dx)

 

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted February 23, 2013 at 10:09 AM (Answer #1)

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let x+1=t ,dx=dt , x^(n)=(t-1)^(n)=t^(n)-c(n,1)t^(n-1)(-1)+ c(n,2)t^(n-1)(-1)x^(2)+..............+c(n,n-1)t (-1)^(n-1)+ (-1)^(n)

int(x^(n)/(x+1))dx=int (( t^(n)-c(n,1)t^(n-1)(-1)+ c(n,2)t^(n-1)(-1)x^(2)+..............+c(n,n-1)t (-1)^(n-1)+(-1)^(n) )/t) dt

= t^(n)/(n) -c(n,1)t^(n-1)/(n-1)+............+c(n,n-1)t (-1)^(n-1)+)+(-1)^(n) log(t) +c  ,provided n is positive integer.

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