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#1 2013-01-25 07:23:56

White_Owl
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integrate x/sqrt(3x+25)

In my homework for this week I have a question:



If I do a substitution u=3x+25, then I have

Which does not help much.



If I try to find such u that du will eliminate x from numerator, then: du=1/x dx and u have to be ln(x)

Which is also not very helpful...



Finally I run the original integral through Maxima, and it gave me:

Which is very scary and I have no idea how it come to this formula.


So which "u" should I use? How to find such "u"? Or maybe there is another approach I should use? I am completely stuck.

#2 2013-01-25 07:42:10

anonimnystefy
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Re: integrate x/sqrt(3x+25)

Hi White_Owl

Continuing on the first thing you tried:



Can you continue from here?

Last edited by anonimnystefy (2013-01-25 07:49:57)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#3 2013-01-25 09:21:44

White_Owl
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Re: integrate x/sqrt(3x+25)

Ok... Then:


And after substituting back u for x I have:


But now if I differentiate it back:

Where did 9 come from?

#4 2013-01-25 09:55:19

anonimnystefy
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Re: integrate x/sqrt(3x+25)

Hi White_Owl

You have multiplied by 3 instead of dividing by 3 when making the substitution...


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#5 2013-01-26 04:31:27

White_Owl
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Re: integrate x/sqrt(3x+25)


Yes, it does look promising.
Thank you very much.

#6 2013-01-26 13:30:01

anonimnystefy
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Re: integrate x/sqrt(3x+25)

You're welcome! smile


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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