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