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Evaluate the integral:` int(x^2+1)/(x+1)dx`

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nanimaggy | eNoter

Posted September 4, 2013 at 11:10 PM via web

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Evaluate the integral:` int(x^2+1)/(x+1)dx`

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mjripalda | High School Teacher | (Level 3) Educator

Posted September 5, 2013 at 1:02 AM (Answer #1)

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`int(x^2+1)/(x+1)dx`

To solve, expand the integrand by dividing the numerator by the denominator. In doing so, it becomes:

`=int(x - 1 + 2/(x+1) )dx`

`=intxdx-int1*dx+int2/(x+1)dx`

`=intx-intdx+2int1/(x+1)dx`

`=x^2/2-x+2ln|x+1| + C`

Hence, `int(x^2+1)/(x+1)dx = x^2/2-x+2ln|x+1|+C` .

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