calc.Evaluate the integral. int((2e^x)/(sinhx+coshx), x=-10...10))

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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`int_-10^10 (2e^x)/(sinhx + coshx) dx`

`int_-10^10 ((2e^x)(sinhx-coshx))/(sinh^2 x- cosh^2 x) dx`

`= int_-10^10-(2e^x sinhx - 2e^x coshx) dx`

`=2 int_-10^10 -e^x sinhx + e^xcoshx dx`

`= 2 int_-10^10 e^x (e^x-e^-x)/2 + e^x (e^x + e^(-x))/2 dx`

`= 2 int_-10^10 ((e^(2x) - 1 +e^(2x) +1)/2 dx)`

`= 2 int_-10^10 e^(2x) dx ```

`= 2(1/2)e^(2x) = e^(2x) `

`==> e^(-20) - e^(20)`

`= 1/e^20 - e^20 `

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