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in this video were going to talk about how to integrate functions that turn into natural log functions so lets start with this example what is the anti-derivative of 1 over x dx it turns out that this is equal to the natural log of x plus c the derivative of l and x is one over x so the antiderivative of one over x is l and x now we need to put an absolute value around the x you cant have a negative number inside a natural log function so we need the absolute value there now lets try another problem what is the antiderivative of 7 over x dx what would you say well we can move the constant to the front and we know that the anti-derivative of 1 over x dx is ln x so the answer is going to be 7 lnx plus c and so thats all you need to do for this example heres another example what about the antiderivative of one over x plus five dx what do you think we need to do for this problem well this is equal to the natural log of x plus five plus c now you can prove it using u substitution so
