On Fri, Sep 5, 2008 at 6:59 PM, Edwin Woollett <woollett at charter.net> wrote:
> A standard technique to get definite integrals
> is to differentiate a known integral with respect
> to a parameter.
>
> This technique is used first to generate the
> correct answer:
>
> (%i1) display2d : false$
> (%i2) assume( a > 0, w > 0 )$
> (%i3) i1 : 'integrate( exp( -a*x)*cos( w*x ), x , 0 , inf )$
> (%i4) i2 : ev(i1, nouns);
> (%o4) a/(w^2 + a^2)
> (%i5) di2 : ( diff(i2, a), ratsimp(%%) );
> (%o5) (w^2 - a^2)/(w^4 + 2*a^2*w^2 + a^4)
> (%i6) eqn : (-1)*(diff( i1, a) = di2 );
> (%o6) 'integrate( x*%e^-(a*x)*cos( w*x), x, 0, inf)
> = -(w^2 - a^2)/(w^4 + 2*a^2*w^2 + a^4)
>
> but direct use of integrate adds "ind" to the
> correct answer.
>
> (%i7) integrate(x*exp(-a*x)*cos( w*x), x, 0, inf);
> (%o7) ind - (w^2 - a^2)/(w^4 + 2*a^2*w^2 + a^4)
>
> Is this a bug?
>
> Yes this is a bug.
Ray