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juanberrio8a 2022-06-21 Answered
The problem is the integral of
8 x x 4 a 4 d x
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Answers (1)

humusen6p
Answered 2022-06-22 Author has 22 answers
Noting that
I = 8 x x 4 a 4 d x = 4 d ( x 2 ) ( x 2 ) 2 ( a 2 ) 2
Let y = x 2 and b = a 2 , then
I = 4 d y y 2 b 2 = 4 1 2 b ( 1 y b 1 y + b ) d y = 2 b ( ln | y b | ln | y + b | ) + C = 2 a 2 ln | x 2 a 2 x 2 + a 2 | + C = 2 a 2 ln | x 2 + a 2 x 2 a 2 | + C
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