Define p(x)=∫0sin⁡x1+t3 dt  +  ∫sin⁡xx1+t3 dt.p(x)=\int_{0}^{\sin x} \sqrt{1+t^{3}}\,dt\; +\; \int_{\sin x}^{x} \sqrt{1+t^{3}}\,dt.…

Mathematics

Problem

Define p(x)=∫0sin⁡x1+t3 dt  +  ∫sin⁡xx1+t3 dt.p(x)=\int_{0}^{\sin x} \sqrt{1+t^{3}}\,dt\; +\; \int_{\sin x}^{x} \sqrt{1+t^{3}}\,dt. Determine p′(x)p'(x) for all real xx.

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