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#1 2013-01-24 08:23:56

White_Owl
Member
Registered: 2010-03-03
Posts: 99

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.

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#2 2013-01-24 08:42:10

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,600

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 (2013-01-24 08:49:57)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#3 2013-01-24 10:21:44

White_Owl
Member
Registered: 2010-03-03
Posts: 99

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?

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#4 2013-01-24 10:55:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,600

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

Hi White_Owl

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


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#5 2013-01-25 05:31:27

White_Owl
Member
Registered: 2010-03-03
Posts: 99

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


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

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#6 2013-01-25 14:30:01

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,600

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

You're welcome! smile


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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