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Janet Forbes 2022-07-08 Answered
Find this definite integral
1 2 e 1 / x x 4 d x
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Answers (1)

Kaya Kemp
Answered 2022-07-09 Author has 18 answers
I think you made an algebra mistake when integrating by parts. Starting with
u 2 e u d u ,
your choice of g = u 2 , d f = e u d u is good. This yeilds
u 2 e u d u = u 2 e u 2 u e u d u = u 2 e u 2 u e u d u .
Next, we focus on u e u d u. Like you suggested, we pick g = u , d f = e u d u. This gives us
u e u d u = u e u e u d u = u e u e u + c .
Putting everything together, we have
u 2 e u d u = u 2 e u 2 ( u e u e u + c ) = e u ( u 2 2 u + 2 ) + c .
I think you forgot to correctly distribute the factor of 2, and a minus sign.

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