SOLUTION: Please help me solve this problem: 3a. The antiderivative of f(x)=2/x is written as f(x)=2In|x|. Why must the absolute value symbol be used? 3b. By applying the rules for n

Question 1014579: Please help me solve this problem:
3a. The antiderivative of f(x)=2/x is written as f(x)=2In|x|. Why must the absolute value symbol be used?
3b. By applying the rules for natural logarithms, how could the answer in question 3a. be expressed so that the absolute value symbol is not required?
Thank-you, your help is always appreciated!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
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3a) ln(x) is defined only for x > 0, hence |x| ensures x > 0
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3b) Take the integral
integral 2/x dx
Factor out constants
2 integral 1/x dx
The integral of 1/x is log(x), therefore
Antiderivative of 2/x = 2log(x)+constant where x > or equal to 1
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