Mathematics

Evaluate $$\int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}dx$$


SOLUTION
Let $$e^x + e^{-x} = t$$
Then $$e^x - e^{-x} = dt$$

Therefore, required integral = $$\int \dfrac{1}{t} dt$$
$$=\ln|t| + C$$
$$=\boxed{\ln(e^x + e^{-x}) + C}$$
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Subjective Easy Published on 17th 09, 2020
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