Tavola degli integrali indefiniti di funzioni iperboliche

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Questa pagina contiene una tavola di integrali indefiniti di funzioni iperboliche. Per altri integrali vedi Integrale § Tavole di integrali.

sinhcxdx=1ccoshcx
coshcxdx=1csinhcx
sinh2cxdx=14csinh2cxx2
cosh2cxdx=14csinh2cx+x2
sinhncxdx=1cnsinhn1cxcoshcxn1nsinhn2cxdx(per n>0)
anche: sinhncxdx=1c(n+1)sinhn+1cxcoshcxn+2n+1sinhn+2cxdx(per n<0n1)
coshncxdx=1cnsinhcxcoshn1cx+n1ncoshn2cxdx(per n>0)
anche: coshncxdx=1c(n+1)sinhcxcoshn+1cxn+2n+1coshn+2cxdx(per n<0n1)
dxsinhcx=1clog|tanhcx2|
anche: dxsinhcx=1clog|coshcx1sinhcx|
anche: dxsinhcx=1clog|sinhcxcoshcx+1|
anche: dxsinhcx=1clog|coshcx1coshcx+1|
dxcoshcx=2carctanecx
dxsinhncx=coshcxc(n1)sinhn1cxn2n1dxsinhn2cx(per n1)
dxcoshncx=sinhcxc(n1)coshn1cx+n2n1dxcoshn2cx(per n1)
coshncxsinhmcxdx=coshn1cxc(nm)sinhm1cx+n1nmcoshn2cxsinhmcxdx(per mn)
anche: coshncxsinhmcxdx=coshn+1cxc(m1)sinhm1cx+nm+2m1coshncxsinhm2cxdx(per m1)
anche: coshncxsinhmcxdx=coshn1cxc(m1)sinhm1cx+n1m1coshn2cxsinhm2cxdx(per m1)
sinhmcxcoshncxdx=sinhm1cxc(mn)coshn1cx+m1mnsinhm2cxcoshncxdx(per mn)
anche: sinhmcxcoshncxdx=sinhm+1cxc(n1)coshn1cx+mn+2n1sinhmcxcoshn2cxdx(per n1)
anche: sinhmcxcoshncxdx=sinhm1cxc(n1)coshn1cx+m1n1sinhm2cxcoshn2cxdx(per n1)
xsinhcxdx=1cxcoshcx1c2sinhcx
xcoshcxdx=1cxsinhcx1c2coshcx
tanhcxdx=1clog|coshcx|
cothcxdx=1clog|sinhcx|
tanhncxdx=1c(n1)tanhn1cx+tanhn2cxdx(per n1)
cothncxdx=1c(n1)cothn1cx+cothn2cxdx(per n1)
sinhbxsinhcxdx=1b2c2(bsinhcxcoshbxccoshcxsinhbx)(per b2c2)
coshbxcoshcxdx=1b2c2(bsinhbxcoshcxcsinhcxcoshbx)(per b2c2)
coshbxsinhcxdx=1b2c2(bsinhbxsinhcxccoshbxcoshcx)(per b2c2)
sinh(ax+b)sin(cx+d)dx=aa2+c2cosh(ax+b)sin(cx+d)ca2+c2sinh(ax+b)cos(cx+d)
sinh(ax+b)cos(cx+d)dx=aa2+c2cosh(ax+b)cos(cx+d)+ca2+c2sinh(ax+b)sin(cx+d)
cosh(ax+b)sin(cx+d)dx=aa2+c2sinh(ax+b)sin(cx+d)ca2+c2cosh(ax+b)cos(cx+d)
cosh(ax+b)cos(cx+d)dx=aa2+c2sinh(ax+b)cos(cx+d)+ca2+c2cosh(ax+b)sin(cx+d)

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