integrate x/sqrt(3x+25)

White_Owl · 2013-01-24 08:23:56

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.

anonimnystefy · 2013-01-24 08:42:10

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)

White_Owl · 2013-01-24 10:21:44

Ok... Then:

And after substituting back u for x I have:

But now if I differentiate it back:

Where did 9 come from?

anonimnystefy · 2013-01-24 10:55:19

Hi White_Owl

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

White_Owl · 2013-01-25 05:31:27

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

anonimnystefy · 2013-01-25 14:30:01

You're welcome!

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