Find: ∫ (x^-1)/(( log x )^2-5 log x +4) d x

Let $\displaystyle \log \mathrm{x}=\mathrm{t} ; \frac{1}{\mathrm{x}} \mathrm{dx}=\mathrm{dt}$ Given integral $\displaystyle =\int \frac{1}{\mathrm{t}^{2}-5 \mathrm{t}+4} d \mathrm{t}$ $$=\int \frac{1}{\left(\mathrm{t}-\dfrac{5}{2}\right)^{2}-\left(\dfrac{3}{2}\right)^{2}} d \mathrm{t} $$ $$=\frac{1}{3} \log \left|\frac{\mathrm{t}-4}{\mathrm{t}-1}\right|+C $$ $$=\frac{1}{3} \log \left|\frac{\log \mathrm{x}-4}{\log \mathrm{x}-1}\right|+C $$