Home/Calculus II/Useful forms/Formula8.6. Useful formsFormulaIn 8.6. Useful formsFormulaCopy LaTeX∫dxx2+a2=1aarctan (xa)+C,a>0\int\frac{dx}{x^2+a^2} =\frac{1}{a}\arctan\!\left(\frac{x}{a}\right)+C, \qquad a>0∫x2+a2dx=a1arctan(ax)+C,a>0Tagsantiderivativepartial fractionspartial fractions: useful formsfunctions rationalVariablesCCCConstante real de integraciónxxxVariable independiente (variable de integración)aaaConstante real (a menudo a>0a>0a>0)dxdxdxDiferencial respecto de xxxConditionsa>0a>0a>0Found an error? Contact us.Related formulasRelatedFormula∫dx(x−r)n=−1(n−1)(x−r)n−1+C,n>1\int\frac{dx}{(x-r)^n} =-\frac{1}{(n-1)(x-r)^{n-1}}+C, \qquad n>1∫(x−r)ndx=−(n−1)(x−r)n−11+C,n>1Open formulaOpen in sectionRelatedFormula∫dxx−r=ln∣x−r∣+C\int\frac{dx}{x-r}=\ln|x-r|+C∫x−rdx=ln∣x−r∣+COpen formulaOpen in section