# How do you integrate #int(x)/((3x-2)(x+2)(2x-1))# using partial fractions?

#1/4ln|3x-2| - 1/20ln|x+2| -1/5ln|2x-1| + c#

Since the factors on the denominator are linear , the numerators will be constants , say A , B and C.

Now multiply through by (3x-2)(x+2)(2x-1)

hence : x = A(x+2)(2x-1) + B(3x-2)(2x-1) + C(3x-2)(x+2)...(1)

hence integral becomes

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To integrate ( \frac{x}{(3x-2)(x+2)(2x-1)} ) using partial fractions, you first decompose the fraction into partial fractions. After decomposing, you equate the original fraction to the sum of the partial fractions and then solve for the constants. Once you have the partial fractions, you integrate each term separately.

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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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