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# Find the integral of 1/(x log x)

Evaluate the following integral: First, we add and subtract in the numerator, For the integral on the left, let then and so we have Therefore, we have 1. Preet Malviya says:

If we do the above integration by integration by parts we 1/x as second function and logx as first function we end up with the expression I = 1 + I , so can you tell me what’s wrong with this method ?

• Freddy says:

bro jus take logx=t and differentiate it therefore it becomes 1/x = dt/dx which can be written as dx/x = dt now substitute in the question we get int 1/t dt now we know int of 1/t is log(t) + c
substitute t we get log(logx)+c

the above method is lengthy and most prolly has the tendency to make teachers tear your answer sheets

2. Anonymous says:

Thank you for the help

3. Anonymous says:

what if you just let u = log x du = 1/x dx so then you have the integral of 1/u du, integrate and you get log u + c. subsititute to obtain: log | log x| + c

4. chuck says:

need help to find the integral ln(x)/(x+a). Really appreciate it if you can show the integral can be expressed in elementary functions.