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Question
The anti derivative of `(sqrt(x) + 1/sqrt(x))` is 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`
MCQ
Solution
`2/3 x^(3/2) + 2x^(1/2) + c`
Explanation:
`int (sqrt(x) + 1/sqrt(x)) dx = int sqrt(x) dx + int 1/sqrt(x) dx`
= `int x^(1/2) dx + int x^(-1/2) dx`
Now, `int x^n dx = (x^(n + 1))/(alpha^(n + 1))`
∴ `int (sqrt(x) + 1/sqrt(x)) 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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