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Question Number 186051 by Tom last updated on 31/Jan/23

$$\underset{-1}{\stackrel{0}{\int }}\mid 5^x-5^{-x}\mid dx$$

Answered by Frix last updated on 31/Jan/23

$$=\underset{-1}{\stackrel{0}{\int }}\mid 2\sinh \left(x\ln 5\right)\mid dx=$$$$=-2\underset{-1}{\stackrel{0}{\int }}\sinh \left(x\ln 5\right)dx=$$$$=-\frac{2}{\ln 5}{\left[\cosh \left(x\ln 5\right)\right]}_{-1}^0=\frac{16}{5\ln 5}$$

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