The integral shown in the image is:
\int (3x+4) \, dx
To solve this integral, we will use the basic rules of integration.
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Integral of 3x:
- Since the derivative of x^2 is 2x, the integral of x (in terms of x^2) adjusted for the coefficient 3 gives us \frac{3}{2}x^2.
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Integral of 4:
- The integral of a constant is just the constant times the variable of integration, so this would be 4x.
Putting it all together, the integral becomes:
\frac{3}{2}x^2 + 4x + C
where C is the constant of integration.