For the following function​ f, find the antiderivative F that satisfies the given condition.
​f(x)equals=3 StartRoot x EndRoot plus 93x+9​; ​F(1​)equals=6

To find the antiderivative \( F(x) \) of the given function \( f(x) = 3\sqrt{x} + 9x + 9 \) that satisfies \( F(1) = 6 \), follow these steps:

1. **Rewrite the function in a more integrable form:**

   \[
   f(x) = 3\sqrt{x} + 9x + 9
   \]

   The square root term can be rewritten using exponents:

   \[
   3\sqrt{x} = 3x^{1/2}
   \]

   So, the function becomes:

   \[
   f(x) = 3x^{1/2} + 9x + 9
   \]

2. **Find the antiderivative of

Learn how to find the antiderivative of the function f(x) = 3√x + 9x + 9 that satisfies F(1) = 6. This problem involves integrating a function with square root and polynomial terms, applying antiderivative rules and the Fundamental Theorem of Calculus. Suitable for advanced high school students studying calculus.

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