Why does Integral[(e^sqrt(x)) / sqrt(x)] NOT equal e^sqrt(x) + C? Details of how I got there inside...

Why does Integral[(e^sqrt(x)) / sqrt(x)] NOT equal e^sqrt(x) + C? Details of how I got there inside...
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The derivative of sqrt(x) isn’t 1/sqrt(x), it is .5/sqrt(x), because sqrt(x) can be rewritten as x^.5, and the chain rule applies and makes the derivative .5*x^-.5
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