Find the integral of u + 1 u .

Question

Find the integral of $\sqrt{u} + \frac{1}{\sqrt{u}} .$

Smart Achievers · Accepted Answer

(1)

Ans. $\frac{2}{3} u^{3 / 2} + 2 u^{1 / 2} + C$

Explanation:

$\int (\sqrt{u} + \frac{1}{\sqrt{u}}) d u = \int (\sqrt{u}) d u + \int (\frac{1}{\sqrt{u}}) d u$

$= \int (u^{1 / 2}) d u + \int (\frac{1}{u^{1 / 2}}) d u$

$= \frac{u^{3 / 2}}{\frac{3}{2}} + \frac{u^{1 / 2}}{\frac{1}{2}} + C$

$= \frac{2}{3} u^{3 / 2} + 2 u^{1 / 2} + C$

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