Evaluate the following : x+1 x+x d x - Vidyadip

Question

Evaluate the following : $\int \frac{\sqrt{x}+1}{x+\sqrt{x}} \cdot d x$

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Answer

$
\begin{aligned}
& \int \frac{\sqrt{x}+1}{x+\sqrt{x}} \cdot d x \\
= & \int \frac{\sqrt{x}+1}{\sqrt{x}(\sqrt{x}+1)} \cdot d x \\
= & \int \frac{1}{\sqrt{x}} \cdot d x \\
= & 2 \cdot \int \frac{1}{2 \sqrt{x}} \cdot d x \\
= & 2 \sqrt{x}+c
\end{aligned}
$

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