10.-Campo magnètico t4+2bt2=sin2w
I(1)=∫dω/(b-cosw)3/2
salir de polares! b-cosw=t2 dω=tdt/sinw
1-cos2w=1-b2-
I(1)=∫ dt/t2√[(1-b2)-
t4+2bt2)] √(sh2w)
I=∫dt/t2√[(1-b2)-t4+2bt2] t2=b+/-√1 1-(t2-b)2 I=∫dt/t2√[1+(t2-b)]·[1-(t2b)] sumXdif, 2 factores 2ºgrado Aplicamos la proyectiva t=(ax+c)/(x+d) dt=dx/(x+d)2 t2=(a2x2+c2+2acx)/(x2+2dx+d2) +c2+(1-b2)d2] haciendo a2=b2-1 queda √(x+p)
t2+(1-b2)=[(a2+1-b2)x2+2x[ac+d(1-b2)]
p=(c2+d2-b2d2)/2[ac+d(1-b2)] con d=0 p=c/2a
1+b2-t2=[(1+b2-a2)x2+2x(2+a2-ac)+(1+b2)d2-b2] b2+1=a2+2 2x2+2x[a(a-c)+2]+d2(a2+2)-c2 c=a x2+2x-a2/2=0 q=-1+-√(1+a2/2) x+q q=p=1/2 5/2=a2 a=+/-√(5/2) q’=-1-√(1+a2/2)=-5/2 I=∫dx·x-2x2/(x+1)2√(x+p)√[(x+q)(x+q’)]=∫dx/(x+1)2(x+1/2)√(x+5/2) x=v2-5/2 I=∫dv/(v2-3/2)2(v2-2) Numerador de sexto grado: largo y pesado, pero elemental 1/t=v I=∫dv(2-v)/v I(1)=2b·ln(v)-v *********************** b-cosw=t2 dw=tdt/sinw
I(cosω)=∫dωcosω/(b-cosω)3/2=∫tdt(b−t2)/t3√[1-(b2+t42bt2)]=b∫dt/t2√[(1-b2)-t4+2bt2)]-∫dt√[1-(b2+t4-2bt2)]= Aplicamos la proyectiva t=(ax+c)/(x+d) dt=dx/(x+d)2 (t2-b)]·[1-(t2-b)] sumXdif, 2 factores 2ºgrado t2+(1-b2)=[(a2+1-b2)x2+2x[ac+d(1-b2)]+c2+(1-b2)
I(1)=b∫dt/t2√[1+
b2+1=a2+2 como antes
2x2+2x[a(a-c)+2]+d2(a2+2)-c2 c=a x2+2x-a2/2=0 q=-1+-√(1+a2/2) x+q q=p=1/2 5/2=a2 a=√(5/2) queda √(x+p) a=c p=1/2
p=(c2+d2-b2d2)/2[ac+d(1-b2)] con d=0
p=c/2a= con
I(1)=b∫dx·x-2x2/(x+1)2√(x+p)√[(x+q)(x+q’)]= ∫dx/ (x+1)2(x+1/2)√(x+5/2) x=v2-5/2 I=∫dv/(v2-3/2)2(v2-2) 1/t=v I(1)=2b·ln(v)-v
I=∫dv(2-v)/v
v=1/(1+x) como antes
I(2)=∫dt√[1-(b2+t4-2bt2)]=∫dx/x2(2x+1) h=1/x I=∫dh(2+h)/h=2ln(h)
+h I=2bln(v)-v+2ln(h)-h=-b·ln(t2)-1/t-2ln(x)-1/x