Question

calcule a integral de ∫(√(2y ) - 1/√2y)

Answer 1

$\displaystyle I=\int \sqrt{2y}-\dfrac{1}{\sqrt{2y}}\,dy\\ \\ I=\sqrt{2}\int \sqrt{y}\,dy-\dfrac{1}{\sqrt{2}}\int\dfrac{1}{\sqrt{y}}\,dy\\ \\ I=\sqrt{2}\cdot \dfrac{2}{3}\sqrt{y}^3-\dfrac{2}{\sqrt{2}}\sqrt{y}+C\\ \\ \boxed{I=\dfrac{2\sqrt{2}}{3}\sqrt{y}^3-\sqrt{2y}+C}$