Integrating x²dx÷1-x
Integrating a rational function like x²dx÷1-x involves using partial fraction decomposition to break it down into simpler fractions that can be integrated more easily.

Partial Fraction Decomposition
To start, we express the given function as a sum of simpler fractions using the method of partial fraction decomposition.

Finding the Partial Fractions
We express x²dx÷1-x as A/(1-x) + B for constants A and B.

Find the Values of A and B
We find the values of A and B by equating the numerators of the fractions and obtaining a system of equations to solve for A and B.

Integration
Once we have found the values of A and B, we can integrate each term separately.

Integrate A/(1-x) + B
Integrating A/(1-x) with respect to x gives -A * ln|1-x|, and integrating B with respect to x gives Bx.

Final Result
Combining the results of the integrals of A/(1-x) and B, we get the final result of the integration of x²dx÷1-x as -A * ln|1-x| + Bx + C, where C is the constant of integration.