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in this video were going to talk about how to find the indefinite integral of logarithmic functions like this one what is the integral of log base 4 of x it turns out that there is a formula you could use the integral of log base a of u d u is equal to u times log base a u divided by e where e is a constant 2.7182818 and that number divided by u prime now this works if that is if u is a linear function so this could be like 5x x 3x plus 4 and so forth if u is equal to x cubed plus 9 thats not a linear function its not going to work so just keep that in mind so in this example we can see that u is equal to x a is four and u prime the derivative of x is one so the answer is going to be u x log base a or four of u over e so thats going to be x over e divided by u prime which is 1. and so we dont need to write one and then plus the constant of integration so this is the integral of log base 4 of x so thats the simplest way to get the answer using the formula but lets talk about how
