[tex]\text{Avand in vedere ca e vorba despre o arie rezultatul nu poate fi 0.}\\
(\text{cu toate ca asa ar fi dat daca calculam direct.) }\\
\text{Fiind o functie impara,putem trage concluzia ca }\\
\displaystyle \int_{-1}^1 f(x)dx=2\int_0^1 f(x)dx\\
\text{Prin urmare :}\\
A=2\int _{0}^{1} \dfrac{x^3}{1+x^4}dx= \dfrac{1}{2} \int_0^1 \dfrac{4x^3}{1+x^4}dx=\dfrac{1}{2} \ln(1+x^4)|_0^1=calcule =\\
=\dfrac{1}{2}\ln 2=\boxed{\ln \sqrt 2} [/tex]