Mathematics

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


SOLUTION
$$\displaystyle I=\int \frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}dx$$
Let - $$(e^{x}+e^{-x})=f$$
$$(e^{x}-e^{-x})dx=df$$
$$(e^{x}-e^{-x})dx=df$$
$$\therefore \displaystyle I =\int \frac{df}{f}$$
$$= \log f+C$$
substituting value of 1-
$$\therefore I=\log |e^{x}+e^{-x}|+C$$
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Subjective Medium Published on 17th 09, 2020
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