Home/Calcolo II/Integrali trigonometrici/Funzioni iperbolicheSezione 6.8Funzioni iperbolicheFormulaCopia LaTeXsenhx=ex−e−x2,coshx=ex+e−x2\operatorname{senh} x=\frac{e^x-e^{-x}}{2}, \qquad \cosh x=\frac{e^x+e^{-x}}{2}senhx=2ex−e−x,coshx=2ex+e−xcoshx=ex+e−x2\cosh x=\frac{e^x+e^{-x}}{2}coshx=2ex+e−xVedi dettaglio →FormulaCopia LaTeXcosh2x−senh2x=1\cosh^2x-\operatorname{senh}^2x=1cosh2x−senh2x=1Vedi dettaglio →FormulaCopia LaTeXddxsenhx=coshx,ddxcoshx=senhx\frac{d}{dx}\operatorname{senh} x=\cosh x, \qquad \frac{d}{dx}\cosh x=\operatorname{senh} xdxdsenhx=coshx,dxdcoshx=senhxddxcoshx=senhx\frac{d}{dx}\cosh x=\operatorname{senh} xdxdcoshx=senhxVedi dettaglio →FormulaCopia LaTeXddxtanhx=sech2x,ddxcothx=−csch2x\frac{d}{dx}\tanh x=\operatorname{sech}^2x, \qquad \frac{d}{dx}\coth x=-\operatorname{csch}^2xdxdtanhx=sech2x,dxdcothx=−csch2xddxcothx=−csch2x\frac{d}{dx}\coth x=-\operatorname{csch}^2xdxdcothx=−csch2xVedi dettaglio →FormulaCopia LaTeX∫tanhx dx=ln(coshx)+C,∫cothx dx=ln∣senhx∣+C\int\tanh x\,dx=\ln(\cosh x)+C, \qquad \int\coth x\,dx=\ln|\operatorname{senh} x|+C∫tanhxdx=ln(coshx)+C,∫cothxdx=ln∣senhx∣+C∫cothx dx=ln∣senhx∣+C\int\coth x\,dx=\ln|\operatorname{senh} x|+C∫cothxdx=ln∣senhx∣+CVedi dettaglio →
FormulaCopia LaTeXsenhx=ex−e−x2,coshx=ex+e−x2\operatorname{senh} x=\frac{e^x-e^{-x}}{2}, \qquad \cosh x=\frac{e^x+e^{-x}}{2}senhx=2ex−e−x,coshx=2ex+e−xcoshx=ex+e−x2\cosh x=\frac{e^x+e^{-x}}{2}coshx=2ex+e−xVedi dettaglio →
FormulaCopia LaTeXddxsenhx=coshx,ddxcoshx=senhx\frac{d}{dx}\operatorname{senh} x=\cosh x, \qquad \frac{d}{dx}\cosh x=\operatorname{senh} xdxdsenhx=coshx,dxdcoshx=senhxddxcoshx=senhx\frac{d}{dx}\cosh x=\operatorname{senh} xdxdcoshx=senhxVedi dettaglio →
FormulaCopia LaTeXddxtanhx=sech2x,ddxcothx=−csch2x\frac{d}{dx}\tanh x=\operatorname{sech}^2x, \qquad \frac{d}{dx}\coth x=-\operatorname{csch}^2xdxdtanhx=sech2x,dxdcothx=−csch2xddxcothx=−csch2x\frac{d}{dx}\coth x=-\operatorname{csch}^2xdxdcothx=−csch2xVedi dettaglio →
FormulaCopia LaTeX∫tanhx dx=ln(coshx)+C,∫cothx dx=ln∣senhx∣+C\int\tanh x\,dx=\ln(\cosh x)+C, \qquad \int\coth x\,dx=\ln|\operatorname{senh} x|+C∫tanhxdx=ln(coshx)+C,∫cothxdx=ln∣senhx∣+C∫cothx dx=ln∣senhx∣+C\int\coth x\,dx=\ln|\operatorname{senh} x|+C∫cothxdx=ln∣senhx∣+CVedi dettaglio →