Integrate $\int {e}^{3\sqrt x} dx$ ...
let $u = \sqrt x, du = \frac {1}{2\sqrt x}, 2u du = dx$
Then I used integration by parts:
$\int f dg = fg - \int gdf \\ f = u; df = du; \\ dg = e^{3u} du ;g = \int e^{3u} du = \frac 13 e^{3u}\\ \int f dg = fg - \int gdf \Rightarrow \frac 13 e^{3u}u - \frac 13 \int e^{3u}du = \frac 13 e^{3u} (u- \frac 13) + c \Rightarrow \frac 13 e^{3\sqrt x}(\sqrt x - \frac 13) + C $
My question is that why is my answer different from the given answer
$\frac 29 e^{3\sqrt x}(3 \sqrt x -1)$