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Integral Calculus> Integrate : x^2+3/(x^6[x^2+1]) Please hel...

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Integrate : x^2+3/(x^6[x^2+1])Please help

Akshat11 , 10 Years ago

Grade

1 Answers

Sumit Majumdar

Last Activity: 10 Years ago

Dear student,
You can do the following:
$\int \frac{x^2+3}{x^6\left ( x^2+1 \right )} dx=\int \frac{1}{x^6} dx+\int \frac{2}{x^6\left ( x^2+1 \right )} dx$
Now using the partial fraction, we get:
$\frac{2}{x^6\left ( x^2+1 \right )} =\frac{A}{x^2+1}+\frac{B}{x^2}+\frac{C}{x^4}+\frac{D}{x^6}$
Solving for the constants, would give the required result.
Regards

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