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This video explains how to find the indefinite integral of a logarithmic function, specifically log base 4 of x. The formula to use is integral of log base a of u du equals u times log base a u divided by e, where e is a constant. This formula works for linear functions, not for non-linear ones like x cubed plus 9. In the example provided, u equals x, a equals four, u prime equals one, giving the answer as x log base 4 of x over e, plus the constant of integration. This is the simplest way to find the integral using the formula.