Answer
$136$
Work Step by Step
Let $u=x+2$.
So the limits of integration of the definite integral with respect to $u$ are:
$$x=1 \to u=1+2=3$$ $$x=3 \to u=3+2=5$$ $$du=(x+2)'dx=((x)'+(2)')dx=(1+0)dx=dx$$
So the given integral becomes:
$$\int_{3}^{5}u^{3}du$$
Using the $FTC I$ it follows:
$$\int_{3}^{5}u^{3}du=[\frac{u^{4}}{4}]_{3}^{5}=\frac{5^{4}}{4}-\frac{3^{4}}{4}=136$$
