Integration of Rational functions: Example1

Find

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Solution. Since the degree of the numerator is higher than the denominator, we should perform the long-division. We get

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which implies

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We concentrate on the fraction tex2html_wrap_inline165 . The partial decomposition technique gives

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This gives x + 2 = A(x-1) + B(x+1). If we substitute x=1, we get B = 3/2 and we substitute x=-1, we get A = -1/2. Therefore, we have

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Now we are in position to perform the desired integration. Indeed, we have

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Since we have tex2html_wrap_inline89 ,

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we get

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