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Question Number 21076 by j.masanja06@gmail.com last updated on 11/Sep/17

$$integratewithrespecttox$$$$\int x^{sinx}$$

Answered by FilupS last updated on 17/Sep/17

$$\int x^{\sin \left(x\right)}dx=\int e^{\sin \left(x\right)\ln \left(x\right)}dx$$$$=\int \underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{{\sin }^n\left(x\right){\ln }^n\left(x\right)}{n!}dx$$$$=\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{n!}\int {\sin }^n\left(x\right){\ln }^n\left(x\right)dx$$$$=???$$

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