Home/Calculus II/Elementary rules/Formula2.2. Elementary rulesFormulaIn 2.2. Elementary rulesFormulaCopy LaTeX∫ekx dx=ekxk+C,k≠0\int e^{kx}\,dx=\frac{e^{kx}}{k}+C,\qquad k\neq0∫ekxdx=kekx+C,k=0Tagsantiderivativeintegral indefiniteintegral indefinite rules elementarypropertyVariablesCCCConstante real de integraciónkkkConstante real distinta de cero (en muchos contextos)dxdxdxDiferencial respecto de xxxeeeBase of the natural logarithmConditionsk≠0k\neq0k=0Found an error? Contact us.Related formulasRelatedFormula∫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 sectionRelatedFormula∫dxx=ln∣x∣+C\int \frac{dx}{x}=\ln|x|+C∫xdx=ln∣x∣+COpen formulaOpen in sectionRelatedFormula∫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 section