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

This one is actually extremely easy. Notice that 1/(xlogx) = (1/x) / logx. Then this is just S( d/dx(logx) / logx ). By equation 6.16, this is log|logx| + C.

Use substitution with u = log(x) and du = 1/x*dx and voila you’re done!

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.