Mathematics

Integrate:$$\displaystyle \int \sqrt{2x }$$dx


SOLUTION
$$\displaystyle\int{\sqrt{2x}dx}$$

$$=\sqrt{2}\displaystyle\int{{x}^{\frac{1}{2}}dx}$$

$$=\sqrt{2}\dfrac{{x}^{\frac{1}{2}+1}}{\frac{1}{2}+1}$$

$$=\sqrt{2}\dfrac{{x}^{\frac{3}{2}}}{\dfrac{3}{2}}$$

$$=\dfrac{2\sqrt{2}x\sqrt{x}}{3}+c$$

$$=\dfrac{2x\sqrt{2x}}{3}+c$$ where $$c$$ is the constant of integration.
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Subjective Medium Published on 17th 09, 2020
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