How to integrate ∫ d u u c − 2 u

Jackson Duncan

Jackson Duncan

Answered

2022-06-25

How to integrate d u u c 2 u

Answer & Explanation

Josie Stephenson

Josie Stephenson

Expert

2022-06-26Added 20 answers

Let x=2u,dx=2du.
d u u c 2 u = 2 d u 2 u c 2 u = d x x c x
Let v = c x , d v = d x 2 c x , x = c v 2
d x x c x = 2 d v c v 2 = 2 c d v 1 ( v c ) 2 = 2 c a r c t a n h ( v c ) + ζ 0
ζ = 2 c a r c t a n h ( v c ) + ζ 0 = 2 c a r c t a n h ( c 2 u c ) + ζ 0
u = c 2 ( 1 tanh 2 ( c 2 ( ζ ζ 0 ) ) ) = c 2 s e c h 2 ( c 2 ( ζ ζ 0 ) ) = c 2 s e c h 2 ( c 2 ( ζ ζ 0 ) )

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