What is #int1/(x^2+5)# ?
When I use an online integral calculator, it's suggesting I use substitution and let #u=x/sqrt(5)#
I don't understand how to get the #sqrt(5)# . Is there an alternative way of solving this?
If not - what does the #sqrt(5)# mean and how do I work this out for similar questions?
When I use an online integral calculator, it's suggesting I use substitution and let
I don't understand how to get the
If not - what does the
2 Answers
May 16, 2017
Apologies - I've posted this in the wrong place and can't see how to delete it. :(
Jun 27, 2017
(1/sqrt 5) arctan (x / sqrt 5) + C
Explanation:
This is mostly algebraic manipulation and the knowledge that the integral of 1 / ( x^2 + a^2) = 1/a arctan x/a
In this case a = sqrt 5 if a^2 = 5
The substitution comes about to convert x^2 + 5 to u^2 + 1 and using the knowledge that integral of 1 / x^2 + 1 = arctan x
Don't forget that if u = x/(sqrt 5) then dx = (sqrt 5) du
