∫D0− b x + aC−−−−−−−√K1(− b x + aC−−−−−−−√)d x
ersetzen:
− b x + aC= t
−CB∫− b d+ aCACT√K1(T√)dt _
ersetzen:
t =X2
−CB∫− b d+ aC√AC√2X2K1( x )d x
Nach Teilen:
− 2K0(−b dC+AC−−−−−−−−√) d+ 2ABK0(−b dC+AC−−−−−−−−√) −2ABK0(AC−−√) −4CB∫− b d+ aC√AC√K0( x ) xd x
und nach Teilen:
∫− b d+ aC√AC√K0( x ) xd x=K1(AC−−√)AC−−√−K1(− b d+ aC−−−−−−−√)− b d+ aC−−−−−−−√
dann haben wir:
∫D0− b x + aC−−−−−√K1(− b x + aC−−−−−√)d x=1B( ( - 2b d+ 2a )K0(− b d+ aC−−−−−√) +4K1(− b d+ aC−−−−−√)− b d+ aC−−−−−√c - 4K1(AC−−√)AC−−√c - 2K0(AC−−√) ein)
Maple- Code:
int(sqrt((-b*x + a)/c)*BesselK(1, sqrt((-b*x + a)/c)), x = 0 .. d) = ((-2*b*d + 2*a)*BesselK(0, sqrt((-b*d + a)/c)) + 4*BesselK(1, sqrt((-b*d + a)/c))*sqrt((-b*d + a)/c)*c - 4*BesselK(1, sqrt(a/c))*sqrt(a/c)*c - 2*BesselK(0, sqrt(a/c))*a)/b
Jean Marie
Apac