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Evaluate the following definite integral...

Evaluate the following definite integral: `int_1^2e^(2x)(1/x-1/(2x^2))dx`

Text Solution

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Given `int_1^ 2 (1/x-1/(2x^2))e^(2x)dx`
Let `2x=t=>2dx=dt`
when `x=1,t=2` and when `x=2,t=4`
`:.int_1^ 2 (1/x-1/(2x^2))e^(2x)dx=int_2^4(1/2)(2/t-2/(t^2))e^tdt`
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