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What is the integral of #1/(9+x^2)#?

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Dec 31, 2014

The result should be: #1/3arctan(x/3)+C#

I can take the #9# outside the brackets and solve:

#int1/(9+x^2)dx=int1/(9*(1+x^2/9))dx=#
#=int1/3*1/(1+(x/3)^2)dx/3=#

[Remember that #int1/(1+x^2)dx=arctan(x)+C#]

#=1/3arctan(x/3)+C#

You can check the result deriving it.

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