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ELLet’s integrate this rational function in 1 minute.
The standard approach is to factorise the denominator and use partial fraction decomposition, which is not too bad. But factoring out the highest power of x instead of the lowest one actually leads to a clever substitution that simplifies the solution a great deal.
Some food for thought: What characteristic of the polynomial in the denominator makes this substitution work? Can you generalize this?
#math #calculus #integration #integral
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