Calculate int 5^(x+1)e^(2x-1)dx

klastiesym 2022-10-16 Answered
Calculate 5 x + 1 e 2 x 1 d x
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Answers (2)

getrdone07tl
Answered 2022-10-17 Author has 23 answers
Use integration by parts. Set 2 x = y and you'll get:
5 e 1 5 y 2 e y d y = 5 e 1 5 y 2 d ( e y )
Then
5 e 1 5 y 2 e y d y = 5 e 1 5 y 2 d ( e y ) = 5 e 1 ( 5 y 2 e y ln ( 5 ) 2 5 y 2 e y d y )
Combining the first and the last parts:
5 e 1 5 y 2 e y d y = 5 e 1 ( 5 y 2 e y ln ( 5 ) 2 5 y 2 e y d y )
Cancelling out multipliers and collecting the integral terms:
( 1 + ln ( 5 ) 2 ) 5 y 2 e y d y = 5 y 2 e y
So one shoulf get:
5 y 2 e y d y = 5 y 2 e y 1 + ln ( 5 ) 2
So after that just remember the multiplier 5 e 1 and the original variable 2 x = y
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Kasey Reese
Answered 2022-10-18 Author has 3 answers
Another way to solve:
5 x + 1 e 2 x 1 d x = 5 e ( 5 e 2 ) x d x
( 5 e 2 ) x = u ( 5 e 2 ) x d x = d u ln ( 5 e 2 )
5 e ( 5 e 2 ) x d x = 5 e ln ( 5 e 2 ) d u = 5 e ln ( 5 e 2 ) ( u + C )
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