IMO, this is the simplest approach of those presented here.gomunkul51 said:if the degree of the polynomial in the nominator is equal or higher the the degree of the polynomial in the denominator the you have to do polynomial long division to turn the expression to a whole part plus a rational quotient (a fraction with a polynomial in the nominator of a lesser degree then the polynomial in the denominator).
The formula for integrating x^2/(1-x) is ∫x^2/(1-x) dx = -x - ln(1-x) + C.
To solve the integral of x^2/(1-x), you can use the formula ∫x^2/(1-x) dx = -x - ln(1-x) + C. First, you can use the power rule to integrate x^2, which will give you ⅓x^3. Then, you can use the substitution method and let u = 1-x. This will result in -u - ln(u) + C. Finally, substitute back in the value of u and simplify to get the final answer of -x - ln(1-x) + C.
Yes, there are other ways to solve the integral of x^2/(1-x). You can also use the method of partial fractions, where you break the fraction into smaller parts and integrate each part individually. This method may be more time-consuming, but it can also be useful for more complex integrals.
Yes, you can use a calculator or an online integral calculator to solve the integral of x^2/(1-x). However, it is important to understand the steps and methods of integration to fully grasp the concept and be able to solve more complex integrals.
The integration of x^2/(1-x) can be used in various fields such as physics, engineering, and economics. In physics, it can be used to calculate the work done by a variable force. In engineering, it can be used to determine the displacement of a body subjected to a changing force. In economics, it can be used to calculate the present value of a future cash flow. Overall, integration is a powerful tool in solving real-world problems and understanding the behavior of various systems.