# How do you integrate #1/(x^2 + 9)#?

We will try to put this in the form of the arctangent integral:

So here, we see that:

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To integrate 1/(x^2 + 9), you can use the formula for the integral of a rational function involving a quadratic term in the denominator. This can be done by applying a trigonometric substitution. The integral simplifies to (1/3) * arctan(x/3) + C, where C is the constant of integration.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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