# How do you integrate #int sqrt(-x^2-6x-25)/xdx# using trigonometric substitution?

The function:

Note that:

The function:

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To integrate (\int \frac{\sqrt{-x^2-6x-25}}{x} dx) using trigonometric substitution, you can let (x = -5\sin(\theta) - 3). Then, find (dx) in terms of (d\theta). After substitution, simplify the expression and integrate with respect to (\theta). Finally, convert back to the original variable (x).

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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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