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intsqrty(1-(1)/(y))dy

∫y(1−1y)dy \int \sqrt{y}\left(1-\frac{1}{y}\right) d y

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Full solution

Q. ∫y(1−1y)dy \int \sqrt{y}\left(1-\frac{1}{y}\right) d y
  1. Identify integral: Identify the integral to be solved.\newline∫1−1y dy\int\sqrt{1 - \frac{1}{y}} \, dy
  2. Simplify expression: Simplify the expression under the square root.\newlineLet u=1−1yu = 1 - \frac{1}{y}, then du=1y2dydu = \frac{1}{y^2} dy
  3. Substitute uu and dudu: Substitute uu and dudu into the integral.\newline∫u⋅y2 du\int \sqrt{u} \cdot y^{2} \, du

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