Question

qual a integral de ∫_0^1▒x/(1+x^4 )? o resultado é pi/8

Answer 1

$\displaystyle I=\int_0^1 \frac{x}{1+x^4}dx\\ \\ I=\frac{1}{2}\left.\arctan x^2\right|_0^1\\ \\ I=\frac{1}{2}(\arctan 1 -\arctan 0)\\ \\ I=\frac{1}{2}\left(\frac{\pi}{4}-0\right)\\ \\ \boxed{\boxed{I=\frac{\pi}{8}}}$