Actually the only trig function that pops up is arctan (which is essentially a logarithm). If you use int(1/(x^2+1)) dx = arctan x, a linear change of variables will reduce the quadratic factors to this. Victor On Fri, Dec 16, 2016 at 5:52 PM, Henry Baker <hbaker1@pipeline.com> wrote:
I was hinting at the fact that integrate(A(x)/B(x),x), where A(x), B(x) are polynomials in x, is quite easy when B(x) factors into linear factors; use partial fraction expansion. A lot of trig functions crop up when you are unable or unwilling to move into the complex domain and B(x) has quadratic factors.
At 02:27 PM 12/16/2016, Fred Lunnon wrote:
Numerically speaking, integration is in contrast easier than differentiation ... WFL
On 12/16/16, Henry Baker <hbaker1@pipeline.com> wrote:
2. Some closed form integrals may require polynomial root-finding (or root expressing), so you may not like the look of the resulting expression. E.g., you might find floating point approximations to certain numbers instead of a "perfectly precise" answer.
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