- #1
mingzhang54
- 1
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Homework Statement
this is LFS of a question,which is
(1+x)/(1-x-x^2) dx!
i can not simplefy it at all b4 try to do d integration!
The function (1+x)/(1-x-x^2) is a rational function, meaning it is a ratio of two polynomials. It is commonly referred to as a "partial fraction."
Integrating (1+x)/(1-x-x^2) allows us to find the area under the curve of the function. This can be useful in many applications, such as finding the displacement of an object over time or the total profit of a business over a given period.
The process for integrating (1+x)/(1-x-x^2) involves using partial fraction decomposition to break the function into simpler terms, and then using integration techniques such as substitution or integration by parts to solve each term individually.
One common mistake when integrating (1+x)/(1-x-x^2) is forgetting to include the constant of integration. Another mistake is incorrectly applying the integration techniques, such as forgetting to use the chain rule when using substitution.
Yes, it is possible to integrate (1+x)/(1-x-x^2) without using partial fractions. However, it may be more complicated and require more advanced integration techniques. Using partial fractions is usually the most efficient method for integrating this function.