Mathematics

Evaluate : $$\int \dfrac{e^x+1}{e^x+x} \cdot dx$$


SOLUTION
Let $$t={e}^{x}+x$$
$$\Rightarrow dt={e}^{x}+1.dx$$
$$\int{\dfrac{dt}{t}}=\ln{t}+c$$ where $$c$$ is the constant of integration.
$$\int{\dfrac{{e}^{x}+1}{{e}^{x}+x}dx}=\ln{\left({e}^{x}+x\right)}+c$$
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Subjective Medium Published on 17th 09, 2020
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