How do you evaluate the definite integral #int x/(x^2-1)# from #[2,3]#?

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How do you evaluate the definite integral #int x/(x^2-1)# from #[2,3]#?

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Answer 1 · 2016-10-15T07:25:25

1/2ln(8/3)

Explanation:

#intxdx/(x^2-1)=intxdx/((x+1)(x-1))#
#x/((x+1)(x-1))=A/(x+1)+B/(x-1)#
#x=A(x-1)+B(x+1)#
#x=1 =>1=0+2B ; B=1/2#
#x=-1 =>-1=0-2A ; A=1/2#
#I=intxdx/(x^2-1)=1/2(int1dx/(x+1)+int1dx/(x-1))=1/2(ln(x+1)+ln(x-1))=1/2(ln(x+1)(x-1)#
#x=3 ; I=1/2Ln8#
#x=2 ; I=1/2Ln3#
#I=1/2(ln8-ln3)=1/2ln(8/3)#

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How do you evaluate the definite integral #int x/(x^2-1)# from #[2,3]#?

1 Answer

Explanation:

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