Evaluate $\int^{2}_{-2} \frac{x^2+x^6\sin{6x}}{x^2 +4} dx$

Question

Solve $$\int^{2}_{-2} \frac{x^2+x^6\sin{6x}}{x^2 +4} dx$$

What I did was $$\int^{2}_{-2} \frac{x^2+x^6\sin{6x}}{x^2 +4} dx$$

$$= \int^{2}_{-2} \frac{x^2}{x^2 +4} + \frac{x^6\sin{6x}}{x^2 +4} dx$$

$$= \int^{2}_{-2} 1- \frac{4}{x^2 +4} + \frac{x^6\sin{6x}}{x^2 +4} dx$$

$$=[x]^2_{-2}-[2\arctan{\frac{x}{2}}]^2_{-2} + \int^2_{-2}\frac{x^6\sin{6x}}{x^2 +4} dx$$

I am unable to solve for $$ \int^2_{-2}\frac{x^6\sin{6x}}{x^2 +4} dx$$

Answer 1

$ \int^2_{-2}\frac{x^6\sin{6x}}{x^2 +4} dx$ is zero since $\frac{x^6\sin{6x}}{x^2 +4}$ is an odd function.