Integrating $\frac{1}{\sqrt{2\beta x-\alpha x^2}}$

[dcppc]

Does anyone know how to intergrate \frac{1}{\sqrt{2\beta x-\alpha x^2}}
I went to wolfram and type it in, but it gave me a weird number.

 

[Zurtex]

You went to http://integrals.wolfram.com/ and typed something like this in: 1/Sqrt[a x + b x^2] ? Worked fine for me.

 

[dextercioby]

It can't give u a #,but a function of "x"...

Daniel.

 

[dcppc]

But the answer contain i, so I don't know it that's correct or not
The last time I put in 1/Sqrt[a x^2], it gave me [x log x]/Sqrt[a x^2]
Which I don't think is the right answer

 

[Data]

If you aren't sure whether an indefinite integral is right or not, just differentiate it! If it is then you'll get back your original function (for example, the answer it gave you in your last post is right).

 

[Icebreaker]

According to Wolfram's Integrator, \int 0 dx is 0. I thought it was to be a constant.

 

[dcppc]

I thought the intergral of \frac{1}{\sqrt{a x^2}} is \frac{\ln{x}}{\sqrt{a}}
Also when I substitute 2b as 59, the integrator gave me an different answer

 

[Zurtex]

According to Wolfram's Integrator, \int 0 dx is 0. I thought it was to be a constant.

It never adds the constant.

I thought the intergral of \frac{1}{\sqrt{a x^2}} is \frac{\ln{x}}{\sqrt{a}}
Also when I substitute 2b as 59, the integrator gave me an different answer

\frac{x \log x}{\sqrt{a x^2}} = \frac{x \log x}{x \sqrt{a}}

As it goes that website does have bug I've found but I really doubt you will find them.

 

[dcppc]

Ok, another question when I put in 1/Sqrt[19.66 x-a x^2], I don't know what "0." in that intergral means. Also it has 1. ax and 2. Sqrt[x]
what does 0. 1. 2. means?

 

[dextercioby]

These integrals are simple enough to them by hand.There's no need to use software to do them for you.The integrator from wolfram is excellent,though I've caught him with some functions he woudn't integrate.

Okay,there's a problem with your integrals,though.U have a possibly negative expression under a radical.That's why the result is weird,because it may contain complex functions,though the input is real.I suggest u decide on which intervals u wish to integrate...

Daniel.

 

[saltydog]

Does anyone know how to intergrate \frac{1}{\sqrt{2\beta x-\alpha x^2}}
I went to wolfram and type it in, but it gave me a weird number.

Integrands like these require you to complete the square inside the radical. You'll then get something like:

\sqrt{a^2-(x-b)^2}

in the denominator. In this particular form, the answer can be expressed in terms of the ArcSin function.

 

[dextercioby]

Integrals like these

\int \frac{dx}{\sqrt{ax^{2}+bx+c}},\int \sqrt{ax^{2}+bx+c} \ dx

are always expressible through elementary functions...

While even this one

\int \sqrt{x^{3}+0,0000000000000000000000000000000000000000001} \ dx

cannot;


Daniel.