How do I solve $\int_{-5}^{5} \frac{x^3 \sin^2x}{x^4 +2x^2+1}\,dx$?

HINT

It is an odd function, so the integration should be 0

Hint: Let the integrand be $f(x)$.

We have that $f(-x)=-f(x)$, seen by the term $x^3$.

The integral of an odd function from $-a$ to $a$ is $0$.

The function under integral is odd so

$$\\ \int _{ -5 }^{ 5 } \frac { { x }^{ 3 }\sin ^{ 2 }{ x } }{ x^{ 4 }+2x^{ 2 }+1 } dx=\int _{ -5 }^{ 5 } \frac { { x }^{ 3 }\sin ^{ 2 }{ x } }{ { \left( { x }^{ 2 }+1 \right) }^{ 2 } } dx=0$$