Home/Calculus II/Appendix B: useful equivalences/FormulaB. Appendix B: useful equivalencesFormulaIn B. Appendix B: useful equivalencesFormulaCopy LaTeXarsenh (xa)=ln∣x+x2+a2∣−lna,a>0\operatorname{arsenh}\!\left(\frac{x}{a}\right) =\ln\left|x+\sqrt{x^2+a^2}\right|-\ln a, \qquad a>0arsenh(ax)=lnx+x2+a2−lna,a>0Tagsantiderivativeappendix equivalencesequivalenceVariablesxxxVariable independiente (variable de integración)aaaConstante real (a menudo a>0a>0a>0)ln\lnlnNatural logarithmConditionsa>0a>0a>0Found an error? Contact us.Related formulasRelatedFormula∫dxx2+a2=arsenh (xa)+C\int\frac{dx}{\sqrt{x^2+a^2}} =\operatorname{arsenh}\!\left(\frac{x}{a}\right)+C∫x2+a2dx=arsenh(ax)+COpen formulaOpen in sectionRelatedFormula∫tanx dx=−ln∣cosx∣+C=ln∣secx∣+C.\int\tan x\,dx =-\ln|\cos x|+C =\ln|\sec x|+C.∫tanxdx=−ln∣cosx∣+C=ln∣secx∣+C.Open formulaOpen in section