The correct option is B x^5/x^2 +1 =x^3 x + x/x^2 +1 ∴∫x^5/x^2 +1 dx = x^4/4 x^2/2+1/2 log (x^2 +1)+c ...

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First Fundamental Theorem of Calculus

∫x5/x2+1 d x=

Question

$\int \frac{x^{5}}{x^{2} + 1} d x =$

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Solution

The correct option is B

$\frac{x^{5}}{x^{2} + 1} = x^{3} - x + \frac{x}{x^{2} + 1} ∴ \int \frac{x^{5}}{x^{2} + 1} d x = \frac{x^{4}}{4} - \frac{x^{2}}{2} + \frac{1}{2} l o g (x^{2} + 1) + c$

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