Evaluate the integral. (Remember to use absolute values where appropriate. Remember the constant of integration.)

To evaluate the integral, let's go through a hypothetical example, say \( \int (3x^2 - 4) \, dx \). First, we'll integrate term by term. The integral of \( 3x^2 \) is \( x^3 \) (using the power rule), and the integral of \(-4\) is \(-4x\). Thus, we combine these results: \[ \int (3x^2 - 4) \, dx = x^3 - 4x + C, \] where \( C \) is the constant of integration. Now, if we were handling absolute values, like when dealing with \( \int \frac{1}{x} \, dx \), we would have to consider that the natural logarithm function results in an absolute value. Therefore, \( \int \frac{1}{x} \, dx = \ln |x| + C \). It’s always important to remember these subtleties while solving integrals! Have fun playing with different integrals, and remember to keep those absolute values in mind when they pop up!