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The anti derivative of (x+1x) is equals: -

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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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