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sinx-x-dx-

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Question Number 31858 by NECx last updated on 16/Mar/18
∫((sinx)/x)dx
∫sinxxdx
Commented by abdo imad last updated on 18/Mar/18
we have sinx =Σ_(n=0) ^∞ (((−1)^n )/((2n+1)!)) x^(2n+1) with radius R=∞ ⇒ ((sinx)/x) = Σ_(n=0) ^∞ (((−1)^n )/((2n+1)!)) x^(2n) and ∫((sinx)/x)dx = Σ_(n=0) ^∞ (((−1)^n )/((2n+1)^2 (2n)!)) x^(2n+1) and this serie is convergent ....
wehavesinx=∑n=0∞(−1)n(2n+1)!x2n+1withradiusR=∞⇒sinxx=∑n=0∞(−1)n(2n+1)!x2nand∫sinxxdx=∑n=0∞(−1)n(2n+1)2(2n)!x2n+1andthisserieisconvergent….

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