Question

Pessoal, boa noite!

Porque a resposta da integral $\int\limits 1/x^3 \, dx$ é $- \frac{1}{2x^2}$ ?

Obrigado desde já!

Answer 1

$\int\dfrac{1}{x^{3}}dx=\int x^{-3}dx\\\\\\\int\dfrac{1}{x^{3}}dx=\dfrac{x^{-3+1}}{-3+1}\\\\\\\int\dfrac{1}{x^{3}}dx=\dfrac{x^{-2}}{-2}\\\\\\\int\dfrac{1}{x^{3}}dx=-\dfrac{x^{-2}}{2}\\\\\\\boxed{\boxed{\int\frac{1}{x^{3}}dx=-\dfrac{1}{2x^{2}}}}$

Não adicionei a constante de integração