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Evaluate the following integrals:

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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