Question

Calcule a integral indefinida (4*x^3)/(x^4+1)?

Answer 1

$\int\ \frac{4 x^{3} }{ x^{4+1} } \, dx$

Remove a constante$4*\int\ \frac{ x^{3} }{ x^{4+1} } \, dx$$4*\int\ \frac{1 }{ x^{2} } \, dx$$4* \int\ x^{-2} \, dx$
Regra da potencia     Ex($\int\ { x^{a} } \, dx = \frac{ x^{a+1} }{a+1} a \neq -1$)
$4* \frac{ x^{-2+1} }{-2+1}$
Simplifica$4* \frac{ x^{-2+1} }{-2+1} = -x^{-1}$$4* (-x^{-1} )$$-4 x^{-1}$$4* \frac{1}{x}$$\frac{1*4}{x}$$\frac{-4}{x}$
Resposta$\int\ \frac{4 x^{3} }{ x^{4+1} } \, dx = \frac{-4}{x}+C$

Answer 2

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https://brainly.com.br/tarefa/16488096

$\displaystyle\sf\int\dfrac{4x^3}{x^4+1}dx$

$\rm \underline{\rm fac_{\!\!,}a}~u=x^4+1\implies du=4x^3dx\\\displaystyle\sf\int\dfrac{4x^3}{x^4+1}dx=\int\dfrac{du}{u}=\ell n|u|+k$

$\large\boxed{\boxed{\boxed{\boxed{\displaystyle\sf\int\dfrac{4x^3}{x^4+1}=\ell n|x^4+1|+k}}}}$