How to integrate sqrt((ax+b)/x) dx (square root of linear fractional function)

  • Thread starter Holali
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  • #1
9
0
Hi,
simple question, but difficult to find an answer for me

How to integrate sqrt((ax+b)/x) dx ???
a,b constants and x variable

if it matters, I would be happy if you could solve it just for both a,b >0

Thanks
 

Answers and Replies

  • #2
428
1
Let [itex]u=\frac{ax+b}{x}[/itex]. We're keeping our fingers crossed, there's no other common methods that apply, so this looked like most natural thing to do.

The expression will be a little simpler, but now we try a more common method, which is let [itex]v=\sqrt{u}[/itex]. To find [itex]du[/itex], we usually consider [itex]v^2=u[/itex], to simplify things. I think you will end up with something that you know how to integrate.
 
  • #3
798
34
Hi,
simple question, but difficult to find an answer for me

How to integrate sqrt((ax+b)/x) dx ???
a,b constants and x variable

if it matters, I would be happy if you could solve it just for both a,b >0

Thanks
Let x = (b/a)(sinh(t))²
 
  • #4
go here:


integrals.wolfram.com/index.jsp

and enter

sqrt[(a*x+b)/x]

into the text box
 

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