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How to solve this triple integral?

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

A:

Note: $displaystyleint_{D}e^{x}cos^2theta,dtheta=int_{D}e^{x}cos^2thetasintheta,dtheta+int_{D}e^{x}costhetasin^2theta,dtheta$
$displaystyleint_{D}e^{x}cos^2thetasintheta,dtheta=frac{1}{3}int_{0}^{pi/2}e^{x}cos^3thetasintheta,dtheta$
$displaystyleint_{D}e^{x}costhetasin^2theta,dtheta=-frac{1}{3}int_{0}^{pi/2}e^{x}sinthetacos^3theta,dtheta$

A:

Hint: $$begin{align}int_{0}^{pi/2}int_{0}^{pi}int_{0}^{2pi}xe^{x}cos^2theta,dxdtheta dphi &= int_{0}^{pi/2}int_{0}^{pi}int_{0}^{2pi}xcostheta,dphi,dx,dtheta\&=2int_{0}^{pi/2}int_{0}^{phi}xcosthe
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