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Question
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
Options
`1/3 x^(1/3) + 2x^(1/2) + C`
`2/3 x^(2/3) + 1/2 x^2 + C`
`2/3 x^(3/2) + 2x^(1/2) + C`
`3/2 x^(3/2) + 1/2 x^(1/2) + C`
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Solution
`2/3 x^(3/2) + 2x^(1/2) + C`
Explanation:
`(sqrtx + 1/sqrtx) = int (sqrtx + 1/sqrtx)`
`= int sqrtx dx + int 1/sqrtx`dx
`= int x^(1//2) dx + int x^(-1//2)`dx
`= (x^(1/2 + 1))/(1/2 + 1) + (x^(-1/2 + 1))/(- 1/2 + 1)` + C
`= (x^(3//2))/(3//2) + x^(1//2)/(1//2)` + C
`= 2/3 x^(3//2) + 2x^(1//2)` + C
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