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I have this integral here:

\[\int e^{\sqrt{x}}dx\]

and I wanted to ask, why can't I treat it like I would treat this integral:

\[\int (3x+5)^{5}dx\]

In which I would integrate as if g(x)=3x+5 is a normal x, and then divide by the inner derivative ? I tried it with the upper integral, and it doesn't work, the solution includes another "-1" which I don't understand where comes from....

My incorrect answer would be

\[2\cdot \sqrt{x}\cdot e^{\sqrt{x}}\]

why isn't it ?