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How to solve this triple integral?

$$\int \int \int_{D}xe^x \cos^2 \theta dxdyd\theta $$
There is a lot of help online for single integral but I’m really stuck with this one.

A:

Note: $\displaystyle\int_{D}e^{x}\cos^2\theta\,d\theta=\int_{D}e^{x}\cos^2\theta\sin\theta\,d\theta+\int_{D}e^{x}\cos\theta\sin^2\theta\,d\theta$
$\displaystyle\int_{D}e^{x}\cos^2\theta\sin\theta\,d\theta=\frac{1}{3}\int_{0}^{\pi/2}e^{x}\cos^3\theta\sin\theta\,d\theta$
$\displaystyle\int_{D}e^{x}\cos\theta\sin^2\theta\,d\theta=-\frac{1}{3}\int_{0}^{\pi/2}e^{x}\sin\theta\cos^3\theta\,d\theta$

A:

Hint: $$\begin{align}\int_{0}^{\pi/2}\int_{0}^{\pi}\int_{0}^{2\pi}xe^{x}\cos^2\theta\,dxd\theta d\phi &= \int_{0}^{\pi/2}\int_{0}^{\pi}\int_{0}^{2\pi}x\cos\theta\,d\phi\,dx\,d\theta\\&=2\int_{0}^{\pi/2}\int_{0}^{\phi}x\cos\the
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