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Find `int_0^1 (7x-x^2)/((2-x)(x^2+1))dx`

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roshan-rox | Valedictorian

Posted July 15, 2013 at 1:49 PM via web

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Find `int_0^1 (7x-x^2)/((2-x)(x^2+1))dx`

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aruv | High School Teacher | Valedictorian

Posted July 15, 2013 at 2:21 PM (Answer #1)

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Let us write a partial fraction



comparing the coefficients of `x^2,x and constant ` both side.




solving the above system of equation we have

A=2,B=3 and c=-1



`=int_0^1 2/(2-x)dx+int_0^1(3x)/(x^2+1)dx-int_0^1 1/(x^2+1)dx`

`` `=-ln(2-x)|^1_0+(3/2)int_0^1 (2x)/(x^2+1)dx-tan^(-1)(x)|^1_0`







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