Integrating dx/sqrt(x^2+r^2) - Step-by-Step Guide

[omer21]

how can i integrate this expression

dx/sqrt(x^2+r^2)

in books i found just the answer,but i need the solution step by step

can you help me?

 

[arildno]

Now, let x=ru, where u is your new variable.

Try and simplify after this substitution of variables what you get as your integrand!

 

[omer21]

after simplifying i got this

du/sqrt(u^2+1)

but still i can not see the solution

 

[jgens]

If you don't recognize that integral, another useful substitution might be: x = r * sinh(u). Or, if you're unfamiliar with the hyperbolic functions, try the trigonometric substitution: x = r * tan(u).

 

[omer21]

hyperbolic functions are a little complicated for me so i will try x=r*tan(u)

 

[jgens]

That's the more difficult substitution, but alright!

 

[omer21]

i tried x=r.tan(u) substitution and i got what i want.
thanks...