Question #935b8

1 Answer
Roy E.
Dec 28, 2016

You don't. By inspection and checking by differentiation, the integral is #sqrt(x^2+9)+C#

Explanation:

The key point is that the numerator is, give or take a constant multiplier, the derivative of the expression under the square root in the denominator. So, thinking of the the square root as #(x^2+9)^(-1/2)#, you should immediate think of "adding 1' to the power, giving #(x^2+9)^(+1/2)#. Then, mentally differentiating this last expression, you find, hey presto, that by the chain rule the #x^2# becomes #2x# which nicely cancels the #2# and introduces the #x#.

Perhaps you didn't mean to include the #x# in the numerator?

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