Question:
Evaluate the following integrals:
$\int \frac{1}{x(3+\log x)} d x$
Solution:
Assume $3+\log x=t$
$\mathrm{d}(3+\log \mathrm{x})=\mathrm{dt}$
$\Rightarrow \frac{1}{\mathrm{x}} \mathrm{dx}=\mathrm{dt}$
Put $t$ and dt in given equation we get
$\Rightarrow \int \frac{\mathrm{d} t}{t}$
$=\ln |t|+c .$
But $t=3+\log x$
$=\ln |3+\log x|+c$
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