Final answer:
When evaluating an indefinite integral, always remember to add a constant of integration to the result to account for the family of antiderivatives.
Step-by-step explanation:
When evaluating an indefinite integral, it is important to not forget to add a constant of integration. This constant reflects the family of antiderivatives and accounts for the fact that the indefinite integral represents a general solution. In contrast to differentiating, where you might apply the power rule to decrease the exponent of a variable, integrating typically involves increasing the power and dividing by the new exponent, if applicable. Importantly, after performing the integration, it is not correct to multiply by the variable or differentiate the result again, as those are not steps in the process of finding an indefinite integral.
For example, if you integrate a power of x, such as x^n, you generally apply the power rule in reverse, which involves adding 1 to the exponent and dividing by the new exponent (unless n = -1, in which case the antiderivative is the natural logarithm). Then, you must add the constant of integration to the result to complete the process.