How do you use partial fraction decomposition to decompose the fraction to integrate #(16x^4)/(2x1)^3#?
First do the division, then decompose the remainder term.
We can do a partial fraction decomposition only if the degree of the numerator is less than that of the denominator.
Leads (after some algebra) to:
So we get:
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To decompose the fraction ( \frac{16x^4}{(2x1)^3} ) using partial fraction decomposition, follow these steps:

Write the fraction in the form ( \frac{A}{2x1} + \frac{B}{(2x1)^2} + \frac{C}{(2x1)^3} ).

Multiply both sides of the equation by ( (2x1)^3 ) to clear the denominators.

Expand and collect like terms.

Equate the coefficients of like terms on both sides of the equation.

Solve the resulting system of equations for the unknown coefficients ( A ), ( B ), and ( C ).

Once you have found the values of ( A ), ( B ), and ( C ), substitute them back into the original equation.

Integrate each term separately.

Sum up the integrals of each term to obtain the final result.
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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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