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?
Ted Woollett