Mathematics

$$\displaystyle \int \dfrac{dx}{e^x + e^{-x} +2}$$ is equal to


ANSWER

$$\dfrac{-1}{e^x+1} +C$$


SOLUTION
$$\displaystyle \int \dfrac{dx}{e^x + e^{-x} +2}$$

$$\displaystyle =\int \dfrac{e^x}{e^{2x}+2e^x+1}dx$$
Put $$e^x=t$$

$$\Rightarrow e^xdx=dt$$

$$\displaystyle \therefore I=\int \dfrac{dt}{t^2+2t+1}$$

$$\displaystyle =\int \dfrac{dt}{(t+1)^2}$$

$$=\dfrac{-1}{t+1}+C$$

$$=\dfrac{-1}{e^x+1}+C$$
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Single Correct Medium Published on 17th 09, 2020
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