Answer
$$ \frac{3}{{\sqrt 3 }+1}{x^{\sqrt 3 + 1}} + C$$
Work Step by Step
$$\eqalign{
& \int {3{x^{\sqrt 3 }}} dx \cr
& = 3\int {{x^{\sqrt 3 }}} dx \cr
& \sqrt 3 {\text{ is a constant}}{\text{, then using }}\int {{x^a}} dx = \frac{{{x^{a + 1}}}}{{a + 1}} + C \cr
& = 3\left( {\frac{{{x^{\sqrt 3 + 1}}}}{{\sqrt 3 }+1}} \right) + C \cr
& {\text{simplifying, we get:}} \cr
& = \frac{3}{{\sqrt 3 }+1}{x^{\sqrt 3 + 1}} + C} $$
