Integrate $\int (1 + y^{2}) d x$

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Solution

$\int (1 + y^{2}) d x$
Since the integration is w.r.t. $x$ , thus the $(1 + y^{2})$ is constant here.
Therefore,
$\int (1 + y^{2}) d x$
$= (1 + y^{2}) \int d x$
$= (1 + y^{2}) x + C$
Thus,
$\int (1 + y^{2}) d x = (1 + y^{2}) x + C$
Hence the correct answer is $(1 + y^{2}) x + C$ .

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