Home/Calculus II/Elementary rules/Formula2.2. Elementary rulesFormulaIn 2.2. Elementary rulesFormulaCopy LaTeX∫dxx=ln∣x∣+C\int \frac{dx}{x}=\ln|x|+C∫xdx=ln∣x∣+CTagsantiderivativeintegral indefiniteintegral indefinite rules elementarypropertyVariablesCCCConstante real de integraciónxxxVariable independiente (variable de integración)dxdxdxDiferencial respecto de xxxln\lnlnNatural logarithmFound an error? Contact us.Related formulasRelatedFormula∫xn dx=xn+1n+1+C,n≠−1\int x^n\,dx=\frac{x^{n+1}}{n+1}+C,\qquad n\neq-1∫xndx=n+1xn+1+C,n=−1Open formulaOpen in sectionRelatedFormula∫duu=ln∣u∣+C\int \frac{du}{u} = \ln|u| + C∫udu=ln∣u∣+COpen formulaOpen in sectionRelatedFormula∫ekx dx=ekxk+C,k≠0\int e^{kx}\,dx=\frac{e^{kx}}{k}+C,\qquad k\neq0∫ekxdx=kekx+C,k=0Open formulaOpen in sectionRelatedFormula∫akx dx=akxklna+C,a>0, a≠1, k≠0\int a^{kx}\,dx=\frac{a^{kx}}{k\ln a}+C, \qquad a>0,\ a\neq1,\ k\neq0∫akxdx=klnaakx+C,a>0, a=1, k=0Open formulaOpen in section