Excel in math, science, and engineering

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\[ \int_{\pi/3}^0 3\sin \left( \dfrac z2\right) - 5\cos(\pi - z) \, dz = 6 \int_{\pi/6}^0 \sin u \, du + 5 \int_{2\pi/3}^\pi \cos v \, dv = \, ? \]

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