calc.Evaluate the integral. int((2e^x)/(sinhx+coshx), x=-10...10))
1 Answer
hala718 | High School Teacher | (Level 1) Educator Emeritus
`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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