I got a question. It says find a step by step algorithm to compute the antiderivative of $$\int \frac{P(x) } {(1+x^2)^n} $$. Where P(x) is a polynomial and partial fraction could be used while trigonometric substitution should not be used.
On a certain integral with trigonometric substitution not allowed
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$\begingroup$
integration
trigonometry
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0Algorithm: Long Division over and over again, and then partial fractions once you must. The partial fractions won't be pretty, but are going to be exact if I am not mistaken because we have a quadratic. – 2017-02-12
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0What more do you want? This process is guaranteed to work already. – 2017-02-12