$\int \frac{x^{8} + 4}{x^{4} - 2 x^{2} + 2} d x =$

\frac{x^{5}}{5} - \frac{2 x^{3}}{3} + 2 x + C

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\frac{x^{5}}{5} - \frac{2 x^{3}}{3} - 2 x + C

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\frac{x^{5}}{5} + \frac{2 x^{3}}{3} - 2 x + C

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\frac{x^{5}}{5} + \frac{2 x^{3}}{3} + 2 x + C

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Solution

The correct option is D $\frac{x^{5}}{5} + \frac{2 x^{3}}{3} + 2 x + C$
$\int \frac{(x^{8} + 4 + 4 x^{4}) - 4 x^{4}}{x^{4} - 2 x^{2} + 2} d x = \int \frac{(x^{4} + 2)^{2} - (2 x^{2})^{2}}{(x^{4} - 2 x^{2} + 2)} d x = \int \frac{(x^{4} + 2 - 2 x^{2}) (x^{4} + 2 + 2 x^{2})}{(x^{4} - 2 x^{2} + 2)} d x = \frac{x^{5}}{5} + \frac{2 x^{3}}{3} + 2 x + C$

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Similar questions

f (x) = \int \frac{x^{8} + 4}{x^{4} - 2 x^{2} + 2} d x

f (0) = 0

\frac{x^{8} + 4}{x^{4} + 2 x^{2} + 2}

If f (x) = x^{2} - 1, then find f o f .

Find the degree

1) x⁴/4 -x³+2√2x+3

2) 1/x²(x³-x⁴+x⁸⁾

\int \frac{x^{4} + 4}{x^{2} - 2 x + 2} d x

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