Integral of 1/lnx?

Question

1/lnx dx take the integral pls

I am not saying take the derivative, I can not draw here integral's symbol. 1/lnx dx INTEGRAL

SO, if I could not express this with normal functions, what am I suppose to do?
erf ? si?

Answer 1

Summation of [(lnx) ^ n] / [n(n!)] + C, where n = 1 to infinity.
You cannot express this integral into a simpler one.

Answer 2

No closed form solution exists, but one can get a series solution as follows: Change variables by u = ln x. Then exp^u = x, so exp^u du = dx. So thie new integral in terms of u is of (exp^u)/u. Write exp^u as a series, divid each term by u and integrate. You get

ln u + u + (u^2)/[2*2!] + ... +( u^n)/[n*n!] +....

Replace u with ln x to get the final answer.

Answer 3

I know,the integration is below.Read properly.
Integrate 1/lnx dx= ln|x| +c

Answer 4

You CAN NOT express this integral as a combination of so called elementary functions as e^x ,lnx.sinx,cosx,polynomials etc)

Answer 5

?sqrt(a million+lnx) / xlnx dx = ?sqrt(a million+u) / u du, the place u = lnx = ?v / (v^2 - a million) 2vdv, the place v = sqrt(a million+u), u = v^2 - a million du = 2vdv = ?2 + (a million/(v-a million) - a million/(v+a million)) dv = 2v + ln|v-a million| - ln|v+a million| = 2sqrt(a million+lnx) + ln|lnx| - ln|2+lnx| + c

Answer 6

Impossible to express with usual functions. Don't try!

Answer 7

I have not the answer but have found a site that could be interesting