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