Answer
$(-1,\infty)$
Work Step by Step
Step 1. Factor the inequality as
$x^2(x+1)+4(x+1)\gt0$ or $(x+1)(x^2+4)\gt0$
Then the boundary point is $x=-1$.
Step 2. Using the test points to examine signs across the boundary points, we have
$ ...(-)...(-1)...(+)...$
Thus the solutions are $x\gt-1$
Step 3. We can express the solutions on a real number line as shown in the figure.
Step 4. We can express the solutions in interval notation as $(-1,\infty)$
