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Question Number 102911 by I want to learn more last updated on 11/Jul/20

$$\int \frac{\sin \left(\mathrm{x}\right)}{\mathrm{x}}\mathrm{dx}$$

Commented by prakash jain last updated on 11/Jul/20

$$\mathrm{This}\mathrm{question}\mathrm{has}\mathrm{been}\mathrm{asked}\mathrm{so}\mathrm{many}$$$$\mathrm{times}.\mathrm{Among}\mathrm{most}\mathrm{recent}\mathrm{is}\mathrm{Q}98713$$

Answered by Dwaipayan Shikari last updated on 11/Jul/20

$$\int \frac{1}{x}(x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+....)dx$$$$\int 1-\frac{x^2}{3!}+\frac{x^4}{5!}-\frac{x^6}{7!}+.......dx$$$$x-\frac{x^3}{3.3!}+\frac{x^5}{5.5!}-\frac{x^7}{7.7!}+...=\underset{n=1}{\sum ^{\mathrm{\infty }}}{(-1)}^{n+1}\frac{x^{2n-1}}{(2n-1)(2n-1)!}$$

Commented by I want to learn more last updated on 11/Jul/20

$$\mathrm{Thanks}\mathrm{sir}$$

Answered by Aziztisffola last updated on 11/Jul/20

Commented by I want to learn more last updated on 12/Jul/20

$$\mathrm{Thanks}\mathrm{sir}$$

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