Evaluate the following integrals:

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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