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FizeauV

Answered question

2021-11-08

Calculate the integral

\int (\frac{3}{3} \sqrt{x} + \frac{2}{\sqrt{x}}) d x

hosentak

Skilled2021-11-09Added 100 answers

Step 1
Given integral:

\int (\frac{3}{3} \sqrt{x} + \frac{2}{\sqrt{x}}) d x

Formula used:

\int C f (x) d x = C \int f (x) d x

\int (f (x) \pm g (x)) d x = \int f (x) d x + \int g (x) d x

Step 2
To solve the integral first use the formulas for given integral, and integrate the simplified terms,

\int (\frac{3}{3} \sqrt{x} + \frac{2}{\sqrt{x}}) d x = \int (x^{\frac{1}{2}} + 2 x^{- \frac{1}{2}}) d x

= \int x^{\frac{1}{2}} d x + \int 2 x^{- \frac{1}{2}} d x

= \int x^{\frac{1}{2}} d x + 2 \int x^{- \frac{1}{2}} d x

= \frac{2}{3} x^{\frac{3}{2}} + 2 (\frac{x^{\frac{1}{2}}}{\frac{1}{2}})

= \frac{2}{3} x^{\frac{3}{2}} + 4 x^{\frac{1}{2}} + c

= \frac{2}{3} x^{\frac{3}{2}} + 4 \sqrt{x} + c

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