integration of x^n*cos(a+b*x)
- Subject: integration of x^n*cos(a+b*x)
- From: Barton Willis
- Date: Wed, 7 Jul 2010 17:03:25 -0500
Maybe this works:
(%i28) load(abs_integrate)$
(%i29) exponentialize_int(e,x) := (e : integrate(ratexpand(exponentialize (e)), x), if freeof('integrate,e) then e else false)$
(%i30) push('exponentialize_int, extra_integration_methods)$
(%i33) integrate(x^n * cos(a+b*x),x);
(%o33) -(%e^(-%i*a)*gamma_incomplete(n+1,%i*b*x)*x^(n+1)*(%i*b*x)^(-n-1))/2-(%e^(%i*a)*gamma_incomplete(n+1,-%i*b*x)*x^(n+1)*(-%i*b*x)^(-n-1))/2
--Barton
-----maxima-bounces at math.utexas.edu wrote: -----
>since?Maxima?can?integrate?(x^n*?exp(%i*(a+b*x)),?x)
>it?seems?to?me?it?should?be?able?to?handle
>
>x^n*cos(a+b*x)????which?is?the?real?part?of?that.?And?the?answer?is?the?
>realpart?of?the
>answer?to?the?exp(_)?expression.
>
>??(even?declare([x,a,b,n],real),?assume(x>0))?is?no?help.
>
>RJF
>
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