Integral of dx/(sqrt(d^2+x^2))


by carlosbgois
Tags: dx or sqrtd2, integral
carlosbgois
carlosbgois is offline
#1
Mar30-12, 11:43 AM
P: 47
Hi there. Evaluating the expression [itex]\int\frac{dx}{\sqrt{x^{2}+y^{2}}}[/itex] I can get to the result [itex]ln(\frac{x+\sqrt{x^{2}+y^{2}}}{d})[/itex], but in my book it goes from this directly to [itex]ln (x+\sqrt{x^{2}+y^{2}})[/itex], a result wolframalpha says is valid for 'restricted [itex]x[/itex] values'. What does it mean? What are those restricted values? Why?

Many thanks.
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
DonAntonio
DonAntonio is offline
#2
Mar30-12, 12:50 PM
P: 606
Quote Quote by carlosbgois View Post
Hi there. Evaluating the expression [itex]\int\frac{dx}{\sqrt{x^{2}+y^{2}}}[/itex] I can get to the result [itex]ln(\frac{x+\sqrt{x^{2}+y^{2}}}{d})[/itex], but in my book it goes from this directly to [itex]ln (x+\sqrt{x^{2}+y^{2}})[/itex], a result wolframalpha says is valid for 'restricted [itex]x[/itex] values'. What does it mean? What are those restricted values? Why?

Many thanks.


Well, since this is indefinite integration both the results are correct as their difference is just the constant [itex]-\ln d[/itex].

The question is: where did you get the constant [itex]d[/itex] from??

The result is valid for any values of [itex]x,y, s.t. x^2+y^2\neq 0[/itex]

DonAntonio
carlosbgois
carlosbgois is offline
#3
Mar30-12, 12:54 PM
P: 47
Thank you. 'd' is actually a constant length (the distance from a point p to a disk, in an axis that goes through the center of the disk)


Register to reply

Related Discussions
Prove series is divergent (sqrt(n+1) - sqrt(n))/sqrt(n) Calculus & Beyond Homework 5
Integral: sqrt(1+((x^4-1)/(2x^2))^2) General Math 13
Iterative square root? sqrt(2+sqrt(2+sqrt(... General Math 6
integral of y=sqrt.(x^2+a^2) or y^2=x^2+a^2 Calculus & Beyond Homework 4
integral of x(sqrt(1-x^2)) + 1/2 -x^2/2...IS IT RIGHT? Calculus & Beyond Homework 5