How do you find the indefinite integral of #int sqrt(169x^2–81)/x dx#?
Here,
Let,
So,
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To find the indefinite integral of ( \int \frac{\sqrt{169x^2  81}}{x} , dx ), follow these steps:

Recognize that the integrand can be simplified using trigonometric substitution.

Let ( x = \frac{9}{13} \sec(\theta) ).

Find ( dx ) using the derivative of ( \sec(\theta) ), which is ( \sec(\theta) \tan(\theta) , d\theta ).

Substitute ( x ) and ( dx ) in terms of ( \theta ) into the integral.

Simplify the integrand using trigonometric identities.

Integrate with respect to ( \theta ).

Substitute back ( x ) in terms of ( \theta ) to obtain the result in terms of ( x ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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