Question

evaluate the integral log 10 x/x dx

Answer 1

\[\int\limits_{}^{}\frac{\log_{10}x}{x} dx ?\]

Answer 2

yes

Answer 3

you remember change of base formula
\[\log_{10}x=\frac{lnx}{\ln10}\]
\[\int\limits_{}^{}\frac{lnx}{\ln10}*\frac{1}{x} dx\]
let u=lnx
du=1/x dx
\[\frac{1}{\ln10}\int\limits_{}^{}u du\]

Answer 4

\[\frac{1}{\ln10}*\frac{u^2}{2}+C=\frac{1}{2\ln10}(lnx)^2+C\]

Answer 5

i did not understand the last part?

Answer 6

the substitution?