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Re: I stumped Maple 17..haha! Look inside.

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On May 21, 8:23 am, Anonymous <a...@anon.com> wrote:
> The derivative of 1/ln(3)*arcsinh(exp(x*ln(3))/2)is 3^x/sqrt(4+9^x)...BUT..when I integrate 3^x/sqrt(4+9^x)
> Maple is stumped!  Hope in Maple 18 it's able to integrate it to get 1/ln(3)*arcsinh(exp(x*ln(3))/2).

But Maple 16 can do it if you replace 3^x by exp(x*ln(3)), and that's
what it used when differentiating the first expression:


cayley[~/Jfh] % maple
    |\^/|     Maple 16 (X86 64 LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple
Inc. 2012
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> y:=1/ln(3)*arcsinh(exp(x*ln(3))/2);
                             arcsinh(1/2 exp(x ln(3)))
                        y := -------------------------
                                       ln(3)

> z:=diff(y,x);
                                    exp(x ln(3))
                          z := ----------------------
                                                     2 1/2
                               (4 + exp(x ln(3)) )

> int(z,x);
                           arcsinh(1/2 exp(x ln(3)))
                           -------------------------
                                     ln(3)

--
John Harper

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Thread

I stumped Maple 17..haha!  Look inside. Anonymous <anon@anon.com> - 2013-05-20 20:23 +0000
  Re: I stumped Maple 17..haha!  Look inside. unruh <unruh@invalid.ca> - 2013-05-20 23:06 +0000
    Re: I stumped Maple 17..haha! Look inside. Anonymous <anon@anon.com> - 2013-05-20 23:19 +0000
    Re: I stumped Maple 17..haha! Look inside. Anonymous <anon@anon.com> - 2013-05-20 23:53 +0000
  Re: I stumped Maple 17..haha! Look inside. jfh <john.harper@vuw.ac.nz> - 2013-05-23 14:43 -0700
    Re: I stumped Maple 17..haha! Look inside. Anonymous <anon@anon.com> - 2013-05-25 23:51 +0000

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