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

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Stumbling Robot

A Fraction of a Dot
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Find the integral of * 1/(x log x) *

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### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

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

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 ?

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

Thank you for the help

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

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.