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Integrate the function
$\frac{\cos \sqrt{x}}{\sqrt{x}}$
$\frac{\cos \sqrt{x}}{\sqrt{x}}$
Solution:
2475 Upvotes
Verified Answer
Put $\sqrt{x}=t$, so that $\frac{1}{2 \sqrt{x}} d x=d t$
$\begin{gathered}
\therefore \int \frac{\cos \sqrt{x}}{\sqrt{x}} d x=2=\int \cos t d t=2 \sin t+\mathrm{C} \\
=2 \sin \sqrt{x}+\mathrm{C}
\end{gathered}$
$\begin{gathered}
\therefore \int \frac{\cos \sqrt{x}}{\sqrt{x}} d x=2=\int \cos t d t=2 \sin t+\mathrm{C} \\
=2 \sin \sqrt{x}+\mathrm{C}
\end{gathered}$
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