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The anti derivative of (sqrt(x)+1/(sqrt(...

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`

Text Solution

Verified by Experts

The correct Answer is:
c
`int (sqrt(x) +(1)/(sqrt(x)))dx =int x^(1//2) dx+ int x^(-1//2) dx`
`= (x^(3//2))/(3//2) +(x^(1//2))/(1//2) +c =(2)/(3)x^(3//2) + 2x^(1//2) +c`
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