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Write the antiderivative of (3√x+1/√x). - Mathematics

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Write the antiderivative of `(3sqrtx+1/sqrtx).`

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Solution

antiderivative of `(3sqrtx+1/sqrtx).=int (3sqrtx+1/sqrtx)dx`

Now, we have: 

`int (3sqrtx+1/sqrtx)dx=int3x^(1/2)dx+intx^(-1/2)dx`

`=3xx2/3x^(3/2)+2x^(1/2)+c   (`

`=2x^(3/2)+2x^(1/2)+C`

`=2sqrtx(x+1)+C`

Thus, the antiderivative of ` (3sqrtx+1/sqrtx). is 2sqrtx(x+1)+C` where c is the constant of integration

Concept: Integration as an Inverse Process of Differentiation
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