Question

integral de x^-3dx e a derivada da resposta

Answer 1

$\int\limits {x^{-3}} \, dx$

$\frac{x^{-2}}{-2} +C$

$\boxed{\boxed{- \frac{1}{2x^{2}} +C}}$

Derivada da integral:

$f(x)=- \frac{1}{2x^{2}}$

$f(x)=- \frac{x^{-2}}{2}$

$f'(x)=- \frac{-2x^{-2-1}}{2}$

$f'(x)=- \frac{-\not 2x^{-3}}{\not 2}$

$\boxed{\boxed{f'(x)= x^{-3}}}$