# What is #int (4-x ) / (x^3-6x +4 )#?

#int (4-x)/(x^3-6x+4) dx =#

#=1/3 ln abs(x-2) + (-1-2sqrt(3))/6 ln abs(x+1-sqrt(3))+ (-1+2sqrt(3))/6 ln abs(x+1+sqrt(3)) + C#

Express as a partial fraction decomposition first:

Solve:

Equating coefficients, we get the following simulataneous equations:

Hence:

Hence:

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The integral of ( \frac{4-x}{x^3-6x+4} ) is calculated using partial fraction decomposition followed by integrating each term. The steps involve:

- Factorizing the denominator.
- Performing partial fraction decomposition.
- Integrating each term separately.

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