Evaluate the integral: $\int {\tan }^{3}x{\sec }^{7}xdx$

$\frac{{\sec }^{7}x}{7}+C$

$\frac{{\sec }^{9}x}{9}+\frac{{\sec }^{7}x}{7}+C$

$\frac{{\sec }^{9}x}{9}+C$

$\frac{{\sec }^{9}x}{9}-\frac{{\sec }^{7}x}{7}+C$