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(x + 8)(x-1)/(x 2 -2x+4)

(x+8)(x-1)/(x2-2x+4)

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1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:

Hello student,
Please find the answer to your question below

I = \int \frac{(x+8)(x-1)}{x^2-2x+4}dx
Do the long division of the integrand,
I = \int (\frac {3(3x-4)}{x^2-2x+4}+1)dx
I = 9\int \frac {(2x-2)}{x^2-2x+4}dx-\int \frac{3}{x^2-2x+4}dx+\int dx
I = 18\int \frac {(x-1)}{(x-1)^2+(\sqrt{3})^{2}}dx-\int \frac{3}{x^2-2x+4}dx+\int dx
I = 9log(x^2-2x+4)-\int \frac{3}{x^2-2x+4}dx+\int dx
I = 9log(x^2-2x+4)-\sqrt{3}tan^{-1}(\frac{x-1}{\sqrt{3}})+\int dx
I = 9log(x^2-2x+4)-\sqrt{3}tan^{-1}(\frac{x-1}{\sqrt{3}})+ x + c

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