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Problem 69 Hard Difficulty

Evaluate each line integral using the given curve $C$.
$\int_{C} x^{3} y d x+x z d y+(x+y)^{2} d z ; C$ is the helix $\mathbf{r}(t)=\langle 2 t, \sin t, \cos t\rangle,$ for $0 \leq t \leq 4 \pi$

Answer

$8 \pi\left(48+7 \pi-128 \pi^{2}\right)=-29,991.4$

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