To find the antiderivative of \( \frac{2}{\sqrt{x}} \), let's rewrite it in a more convenient form for integration:

\[
\frac{2}{\sqrt{x}} = 2x^{-\frac{1}{2}}
\]

Now, apply the power rule for integration. The power rule states:

\[
\int x^n \, dx = \frac{x^{n+1}}{n+1} + C \quad \text{(where \( n \neq -1 \))}
\]

Here, \( n = -\frac{1}{2} \). Using the power rule:

\[
\int 2x^{-\frac{1}{2}} \, dx = 2 \cdot \frac{x^{-\frac{1}{2} + 1}}{-\frac{1}{2} + 1} + C = 2 \cdot \frac{x^{\frac{1}{2}}}{\frac{1}{2}} + C
\]

Simplify:

\[
= 2 \cdot 2x^{\frac{1}{2}} + C = 4\sqrt{x} + C
\]

Thus, the antiderivative of \( \frac{2}{\sqrt{x}} \) is:

\[
4\sqrt{x} + C
\]

Would you like further details or have any questions about this?

Here are 5 related questions to explore:
1. What is the antiderivative of \( \frac{3}{\sqrt{x}} \)?
2. How do you integrate \( x^{-3/2} \)?
3. How would you find the definite integral of \( \frac{2}{\sqrt{x}} \) from 1 to 4?
4. What is the antiderivative of \( x^{-1/2} + 1/x \)?
5. How do you compute the derivative of \( 4\sqrt{x} \)?

**Tip**: When dealing with square roots in integrals, it's often helpful to rewrite the expression using fractional exponents.

Explore how to find the antiderivative of 2/(sqrt x) using the power rule of integration. This detailed solution simplifies the expression and applies calculus concepts to provide a step-by-step guide suitable for students in Grades 11-12.

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