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Write the anti derivative of (3sqrt(x...

Write the anti derivative of `(3sqrt(x)+1/(sqrt(x)))` .

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To find the antiderivative of the function \(3\sqrt{x} + \frac{1}{\sqrt{x}}\), we will integrate the expression with respect to \(x\). ### Step-by-Step Solution: 1. **Write the integral**: \[ I = \int (3\sqrt{x} + \frac{1}{\sqrt{x}}) \, dx \] ...
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The anti derivative of (sqrt(x)+(1)/(sqrt(x)))

Write the antidervative of (3sqrt(x)+(1)/(sqrt(x)))

Knowledge Check

  • The anti-derivative of (sqrt(x) + (1)/(sqrt(x))) equals

    A
    `(1)/(3)x^(1//3) + 2x^(1//2) + C`
    B
    `(2)/(3)x^(2//3) + (1)/(2)x^(2) + C`
    C
    `(2)/(3)x^(3//2) + 2x^(1//2) + C`
    D
    `(3)/(2)x^(3//2) + (1)/(2)x^(1//2) + C`

  • The derivative of f(x) = (sqrt(x) + (1)/(sqrt(x)))^(2) is

    A
    `sqrt(x) + (1)/(sqrt(x))`
    B
    `2 ((sqrt(x) + 1)/(sqrt(x)))`
    C
    `1 - (1)/(x^(2))`
    D
    `1 + (1)/(x^(2))`

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    The derivative of sqrt(sqrt(x)+1) is

    ((1+x).3sqrt(x))/(sqrt(x))

    The anti derivative of (sqrt(x)+1/(sqrt(x))) equals (A) 1/3x^(1/3)+2x^(1/2)+C (B) 2/3x^(2/3)+1/2x^2+C (C) 2/3x^(3/2)+2x^(1/2)+C (D) 3/2x^(3/2)+1/2x^(1/2)+C

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