The purpose of simplifying 1/x(1-x) for integration is to make the integral easier to solve and to find the antiderivative of the expression.
To simplify 1/x(1-x) for integration, you can use algebraic manipulation and the properties of logarithms to rewrite the expression into a simpler form.
Algebraic manipulation allows us to rewrite the expression in a way that makes it easier to integrate. By utilizing algebraic properties, we can transform the expression into a simpler form that can be easily solved.
No, simplifying 1/x(1-x) for integration is an essential step in solving the integral. Skipping this step may result in an incorrect solution or a more complicated integral to solve.
The final result after simplifying 1/x(1-x) for integration will depend on the integral you are trying to solve. However, it will most likely involve natural logarithmic functions and trigonometric functions.