# Find {eq}\int \frac{1}{x^4 - x^3} \, \mathrm{d}x {/eq}.

## Question:

Find {eq}\int \frac{1}{x^4 - x^3} \, \mathrm{d}x {/eq}.

## Partial Fractions:

A proper rational fraction can be transformed into the sum of proper rational fractions by applying the method of decomposition into partial fractions. If the denominator of the rational fraction has three equal real roots x=t, the sum is obtained:$$\frac{a}{x-t} +\frac{b}{(x-t)^2} +\frac{c}{(x-t)^3}$$

## Answer and Explanation: 1

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Given:

$$\int \ \frac{1}{x^4-x^3} \ dx$$

Express the integrand as a sum of partial fractions. The fraction is proper, decompose into simple...

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