How do you evaluate the integral of $int (cos(lnx))/x dx$ ?

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Answer 1 · 2018-04-15T01:16:52

$intcos(lnx)/xdx=sin(lnx)+C$

A substitution solves this.

$u=lnx$

$du=dx/x$

Then, we have

$intcosudu=sinu+C$

Rewriting in terms of $x$ yields

$intcos(lnx)/xdx=sin(lnx)+C$

How do you evaluate the integral of int (cos(lnx))/x dxint (cos(lnx))/x dx?