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If you’re searching for “integral of 2 x,” here are some possible solutions:

$$\boxed{\int 2x \, dx = x^2 + C}$$

$$\boxed{\int \frac{2}{x} \, dx = 2 \ln |x| + C}$$

$$\boxed{\int (2 + x) \, dx = 2x + \frac{x^2}{2} + C}$$

Below are three potential integrals based on common mathematical usage and the step-by-step solutions for each.

Option 1: \( \displaystyle \int 2x \, dx \)

Using the Power Rule, \( \int x^n \, dx = \frac{x^{n+1}}{n+1} \), we get:

\[\begin{align*} = x^2 + C \end{align*}\]

Thus, the result is:

\[\begin{align*} \int 2x \, dx = x^2 + C \end{align*}\]

Option 2: \( \displaystyle \int \frac{2}{x} \, dx \)

This is a standard integral, as \( \displaystyle \int \frac{1}{x} \, dx = \ln |x| \):

\[\begin{align*} = 2 \ln |x| + C \end{align*}\]

Thus, the result is:

\[\begin{align*} \int \frac{2}{x} \, dx = 2 \ln |x| + C \end{align*}\]

Option 3: \( \displaystyle \int (2 + x) \, dx \)

This integral separates into two simpler integrals:

\[\begin{align*} = \int 2 \, dx + \int x \, dx \end{align*}\]

Solving each term:

\[\begin{align*} = 2x + \frac{x^2}{2} + C \end{align*}\]

Thus, the result is:

\[\begin{align*} \int (2 + x) \, dx = 2x + \frac{x^2}{2} + C \end{align*}\]