Question

Evaluate the integrals

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Answer 1

Explanation:

$\sf \int \left [ {( \sqrt{x} + \frac {1}{\sqrt{x}})}^{2} \right ]dx \\ \\ \sf = \int ( {\sqrt{x}}^{2} + 2 × \sqrt{x} × \frac{1}{\sqrt{x}} + {(\frac{1}{\sqrt{x}})}^{2} ) dx \\ \\ \sf = \int ( x + 2 + \frac{1}{x})dx \\ \\ \sf = \int x dx + \int 2dx + \int {x}^{-1} dx \\ \\ \sf = \frac{{x}^{1+1}}{1 + 1 } + 2{x}^{0+1} + lnx \\ \\ \sf = \frac{{x}^{2}}{2} + 2x + lnx + c$

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