Home/Calculus II/Useful forms/Formula8.6. Useful formsFormulaIn 8.6. Useful formsFormulaCopy LaTeX∫dxx−r=ln∣x−r∣+C\int\frac{dx}{x-r}=\ln|x-r|+C∫x−rdx=ln∣x−r∣+CTagsantiderivativepartial fractionspartial fractions: useful formsfunctions rationalVariablesCCCConstante real de integraciónxxxVariable independiente (variable de integración)dxdxdxDiferencial respecto de xxxrrrRadio o coordenada polarln\lnlnNatural logarithmFound an error? Contact us.Related formulasRelatedFormulaA1x+B1x2+px+q+A2x+B2(x2+px+q)2+⋯+Amx+Bm(x2+px+q)m.\frac{A_1x+B_1}{x^2+px+q} +\frac{A_2x+B_2}{(x^2+px+q)^2} +\cdots +\frac{A_mx+B_m}{(x^2+px+q)^m}.x2+px+qA1x+B1+(x2+px+q)2A2x+B2+⋯+(x2+px+q)mAmx+Bm.Open formulaOpen in sectionRelatedFormula∫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∫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>0Open formulaOpen in section