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Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, in this case $n=1$
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$\int\frac{1}{x}dx=\frac{1}{2}y^2$
Learn how to solve problems step by step online. Solve the differential equation int(1/x)dx=int(y)dy. Applying the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, in this case n=1. Solve the integral \int\frac{1}{x}dx and replace the result in the differential equation. Find the explicit solution to the differential equation. We need to isolate the variable y.