# How do you use substitution to integrate # f(x)= x/sqrt(20+x^2)#?

and undoing the substitution:

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To integrate ( f(x) = \frac{x}{\sqrt{20 + x^2}} ) using substitution:

- Let ( u = 20 + x^2 ).
- Find ( \frac{du}{dx} ) and express ( dx ) in terms of ( du ).
- Substitute ( u ) and the expression for ( dx ) into the integral.
- Express ( x ) in terms of ( u ) within the integral.
- Simplify the integral in terms of ( u ).
- Integrate with respect to ( u ).
- Finally, substitute back ( x ) for ( u ) to express the result in terms of ( 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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