Sir, I have solved the following question: ?logx/x^n dx My answer to this question is: x^(1-n)/(1-n) .logx-x^(1-n)/(1-n)^2 +C But the answer given in the book is: x^(1-n)/(1-n) .log|x|-x^(1-n)/(1-n)^2 +C So please tell me why does the writer uses log|x| and not logx in his answer ?

Asked by Manoj | 26th Mar, 2013, 09:41: AM

Expert Answer:

This is because the log function is not definied for negative values of x and hence, whenever you write logx, you need to write log|x|, in order to make sure that the function is defined. |x| is always positive, it is equal to x if x>=0 and is equal to -x if x<0 and hence, the resulting value is always greater than or equal to 0. 
Please note that the integral of 1/x is always log|x| and not logx, just to define the function in cases where x is negative also. 

Answered by  | 26th Mar, 2013, 10:20: AM

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