Mathematics

Solve: $$\displaystyle \int \dfrac{\cos x}{x}dx$$


SOLUTION
$$ \int \frac{cosx}{x}dx $$ can't be done in elementary 
functions.
But we can use Taylor series 
$$ \Rightarrow cosx = 1-\frac{k^{2}}{2!}+\frac{k^{4}}{4!}-\frac{k^{6}}{6!}+---$$
$$ \Rightarrow \frac{cosx}{x} = \frac{1}{x}-\frac{k}{2!}+\frac{k^{3}}{4!}-\frac{k^{5}}{6!}+---$$
$$\Rightarrow  \int \frac{cosx}{k}dx = lnx-\frac{x^{2}}{2.2!}+\frac{k^{4}}{4.4!}-\frac{k^{6}}{6.6!}+----+C $$ 
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Subjective Medium Published on 17th 09, 2020
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