∫_0 ^1 ((x^4 (1−x)^4 )/(1+x^2 ))dx


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Question Number 166307 by ArielVyny last updated on 18/Feb/22

$\int_{0}^{1} \frac{x^{4} {(1 - x)}^{4}}{1 + x^{2}} d x$
	Answered by MJS_new last updated on 18/Feb/22

	$\underset{0}{\int^{1}} \frac{x^{4} {(1 - x)}^{4}}{x^{2} + 1} d x =$ $= \underset{0}{\int^{1}} (x^{6} - 4 x^{5} + 5 x^{4} - 4 x^{2} + 4 - \frac{4}{x^{2} + 1}) d x =$ $= {[\frac{x^{7}}{7} - \frac{2 x^{6}}{3} + x^{5} - \frac{4 x^{3}}{3} + 4 x - 4 \arctan x]}_{0}^{1} =$ $= \frac{22}{7} - π$
	Commented by ArielVyny last updated on 19/Feb/22

	$e x a c t s i r t h a n k$
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