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Question Number 86998 by M±th+et£s last updated on 01/Apr/20

$$\int \frac{6e^x}{e^{2x}-1}dx$$

Answered by TANMAY PANACEA. last updated on 01/Apr/20

$$\int \frac{6d\left(e^x\right)}{(e^x+1)(e^x-1)}$$$$6\int \frac{dt}{(t+1)(t-1)}$$$$3\int \frac{(t+1)-(t-1)}{(t+1)(t-1}dt$$$$3\int \frac{dt}{t-1}-3\int \frac{dt}{t+1}$$$$3ln\left(\frac{t-1}{t+1}\right)+c$$$$3ln\left(\frac{e^x-1}{e^x+1}\right)+c$$

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