Solve d y d x = xdx - Vidyadip

Question

Solve $\frac{d y}{d x}=\log xdx$

✓

Answer

$
\begin{aligned}
& \frac{d y}{d x}=\log xdx \\
& \therefore d y =\log xdx
\end{aligned}
$
On integrating, we get
$
\begin{aligned}
& \int dy =\int \log x \cdot 1 dx \\
& \therefore y =(\log x ) \int 1 dx -\int\left[\left\{\frac{d}{d x}(\log x)\right\} \cdot \int 1 d x\right] d x \\
& \therefore y =(\log x ) \cdot x -\int \frac{1}{x} \cdot x d x \\
& \therefore y = x \log x -\int 1 dx \\
& \therefore y = x \log x - x + c
\end{aligned}
$
This is the general solution.

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