Mathematics

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


SOLUTION
$$\displaystyle\int\dfrac {\cos \sqrt {x}}{\sqrt {x}}dx$$
Put, $$  \sqrt{x} = t $$

$$\implies \dfrac{1}{2\sqrt{x}} dx = dt$$

$$\implies \dfrac{1}{\sqrt{x}} dx = 2dt$$

Now, $$\displaystyle\int \dfrac{\cos \sqrt{x}}{\sqrt{x}} dx = \int 2 \cos {t} dt$$

$$ = 2\sin t + c$$

$$ = 2\sin {\sqrt{x}} + c$$




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Subjective Medium Published on 17th 09, 2020
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