How to integrate ∫ d u u c − 2 u

Question

How to integrate   ∫            d      u              u              c        −        2        u

Josie Stephenson · Accepted Answer

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    )  )

How to integrate ∫ d u </mrow> u

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