Home/Calculus II/Appendix A: extensive table of antiderivatives/A.5. Hyperbolic integralsContentA.5. Hyperbolic integralsA.5.1 Basic hyperbolic functionsCopy LaTeX∫senh u du=coshu+C\int \operatorname{senh}\,u\,du = \cosh u + C∫senhudu=coshu+CView detail →FormulaCopy LaTeX∫coshu du=senh u+C\int \cosh u\,du = \operatorname{senh}\,u + C∫coshudu=senhu+CView detail →FormulaCopy LaTeX∫tanhu du=ln(coshu)+C\int \tanh u\,du = \ln(\cosh u) + C∫tanhudu=ln(coshu)+CView detail →FormulaCopy LaTeX∫cothu du=ln∣senh u∣+C\int \coth u\,du = \ln|\operatorname{senh}\,u| + C∫cothudu=ln∣senhu∣+CView detail →FormulaCopy LaTeX∫sechu du=arctan(senh u)+C\int \operatorname{sech} u\,du = \arctan(\operatorname{senh}\,u) + C∫sechudu=arctan(senhu)+CView detail →FormulaCopy LaTeX∫cschu du=ln∣tanhu2∣+C\int \operatorname{csch} u\,du = \ln\left|\tanh\frac{u}{2}\right| + C∫cschudu=lntanh2u+CView detail →A.5.2 Derivatives of hyperbolic functions (associated integrals)Copy LaTeX∫sech2u du=tanhu+C\int \operatorname{sech}^2 u\,du = \tanh u + C∫sech2udu=tanhu+CView detail →FormulaCopy LaTeX∫csch2u du=−cothu+C\int \operatorname{csch}^2 u\,du = -\coth u + C∫csch2udu=−cothu+CView detail →FormulaCopy LaTeX∫sechu tanhu du=−sechu+C\int \operatorname{sech} u\,\tanh u\,du = -\operatorname{sech} u + C∫sechutanhudu=−sechu+CView detail →FormulaCopy LaTeX∫cschu cothu du=−cschu+C\int \operatorname{csch} u\,\coth u\,du = -\operatorname{csch} u + C∫cschucothudu=−cschu+CView detail →
A.5.1 Basic hyperbolic functionsCopy LaTeX∫senh u du=coshu+C\int \operatorname{senh}\,u\,du = \cosh u + C∫senhudu=coshu+CView detail →
FormulaCopy LaTeX∫coshu du=senh u+C\int \cosh u\,du = \operatorname{senh}\,u + C∫coshudu=senhu+CView detail →
FormulaCopy LaTeX∫tanhu du=ln(coshu)+C\int \tanh u\,du = \ln(\cosh u) + C∫tanhudu=ln(coshu)+CView detail →
FormulaCopy LaTeX∫cothu du=ln∣senh u∣+C\int \coth u\,du = \ln|\operatorname{senh}\,u| + C∫cothudu=ln∣senhu∣+CView detail →
FormulaCopy LaTeX∫sechu du=arctan(senh u)+C\int \operatorname{sech} u\,du = \arctan(\operatorname{senh}\,u) + C∫sechudu=arctan(senhu)+CView detail →
FormulaCopy LaTeX∫cschu du=ln∣tanhu2∣+C\int \operatorname{csch} u\,du = \ln\left|\tanh\frac{u}{2}\right| + C∫cschudu=lntanh2u+CView detail →
A.5.2 Derivatives of hyperbolic functions (associated integrals)Copy LaTeX∫sech2u du=tanhu+C\int \operatorname{sech}^2 u\,du = \tanh u + C∫sech2udu=tanhu+CView detail →
FormulaCopy LaTeX∫csch2u du=−cothu+C\int \operatorname{csch}^2 u\,du = -\coth u + C∫csch2udu=−cothu+CView detail →
FormulaCopy LaTeX∫sechu tanhu du=−sechu+C\int \operatorname{sech} u\,\tanh u\,du = -\operatorname{sech} u + C∫sechutanhudu=−sechu+CView detail →
FormulaCopy LaTeX∫cschu cothu du=−cschu+C\int \operatorname{csch} u\,\coth u\,du = -\operatorname{csch} u + C∫cschucothudu=−cschu+CView detail →