Use a Table of Integrals to Evaluate the Integral $\int x^{3} \sin \left(x^{2}+3\right) d x$

Multiple Choice

Use a table of integrals to evaluate the integral. $\int x^{3} \sin \left(x^{2}+3\right) d x$

A) $\frac{1}{2} \sin \left(x^{2}+\sqrt{3}\right) -\frac{1}{2} x^{2} \cos \left(x^{2}+\sqrt{3}\right) +C$
B) $\frac{1}{2} \sin \left(x^{2}+3\right) -\frac{1}{2} x^{2} \cos \left(x^{2}+3\right) +C$
C) $-\frac{1}{2} \sin \left(x^{2}+\sqrt{3}\right) -\frac{1}{2} x^{2} \cos \left(x^{2}+\sqrt{3}\right) +C$
D) $-\frac{1}{2} \sin \left(x^{2}+3\right) -\frac{1}{2} x^{2} \cos \left(x^{2}+3\right) +C$