Question

integration of sin x/x ??

Answer 1

Dear student

Taylor Series expansion of sinx is

$$\begin{gathered} \sin x=x-\frac{x^3}{3!}+\frac{x^5}{5!}...\infty \\ \frac{\sin x}{x}=1-\frac{x^2}{3!}+\frac{x^4}{5!}...\infty \\ \int \frac{sinx}{x}dx=\int \left(1-\frac{x^2}{3!}+\frac{x^4}{5!}...\infty \right)dx=x-\frac{x^3}{3\times 3!}+\frac{x^5}{5\times 5!}...\infty \end{gathered}$$

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