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Evaluate: int(e^(3x)+e^(5x))/(e^x+e^(-x)...

Evaluate: `int(e^(3x)+e^(5x))/(e^x+e^(-x))dx`

Text Solution

Verified by Experts

The correct Answer is:
`(e^(4x))/(4)+C`
`I=int(e^(3x)+e^(5x))/(e^(x)+e^(-x)) `
`=int(e^(4x)+e^(6x))/(e^(2x)+1)dx`
`=int(e^(4x)(e^(2x)+1))/(e^(2x)+1)dx`
`=int e^(4x)dx=(e^(4x))/(4)+C`
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