Question

Question #935b8

Answer 1

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?