We need to find

`y=int sqrt(e^(x+3))dx,`

and subsitute our given conditions to find the equation of the curve.

Put `u = x + 3` then `du = dx`. Perform the integral.

`y=intsqrt(e^(x+3)) dx`

`=intsqrt(e^u) du`

`=inte^(u//2) du`

`=2e^(u//2)+K`

`=2e^((x+3)//2)+K`

Now, the curve passes through `(1, 0)`.

This means when `x = 1`, `y = 0`.

So `0=2e^2+K`, giving `K = -2e^2`.

So the required equation of the curve is:

`y=2e^((x+3)//2)-2e^2`

`=2(sqrt(e^(x+3))-e^2)`

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