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

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log⁡e2x−e−2x+C

12log⁡e2x+e−2x+C

log⁡e2x+e−2x+C

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detailed solution

Correct option is B

∫e2x−e−2xe2x+e−2xdx Let e2x+e−2x=t⇒ 2e2x−2e−2x=dtdx⇒ dx=dt2e2x−e−2xe2x−e−2xe2x+e−2xdx=∫e2x−e−2xtdt2e2x−e−2x=12∫1tdt=12log⁡|t|+C=12log⁡e2x+e−2x+C

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∫e2x−e−2xe2x+e−2xdx is equal to

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