Part II: Fill$-$in$-$the$-$Blank $($Use correct and complete notation for proper credit.$)$

$10.(5$ points$)$ Evaluate the integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^2{e}^{2x}dx=$

$11.(5$ points$)$ The interval of convergence for ${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^n\frac{(n+1)!x^n}{n^3}$ is

$12.(5$ points$)$ Rewrite $f(x)=\frac{5x}{4+x^6}$ as a Maclaurin series in summation notation.

$f(x)=$

$(5$ points$)$ Convert the following parametric equation to a Cartesian equation:

$x(t)=\sqrt[3]{t},y(t)=3t+4$

Cartesian equation is

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