Integration of ; ((1/X(4 + Inx))dx?

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Answer 1 · 2018-04-29T01:19:32

$int1/(x(4+lnx))dx=ln|4+lnx|+C$

So, we want to determine

$int1/(x(4+lnx))dx$

This can be solved using a substitution:

$u=lnx$

$du=dx/x$

Rewriting the integral a little, we see that $du$ indeed shows up:

$int1/(4+lnx)*dx/x$

So, apply the substitution:

$int(du)/(4+u)$

We can apply a second brief substitution here:

$v=4+u$

$dv=du$

$int(dv)/v=ln|v|+C$

$=ln|4+u|+C$

Rewrite in terms of $x:$

$int1/(x(4+lnx))dx=ln|4+lnx|+C$