Home/Calculus II/A.1. Basic integration formulas/FormulaA.1. Basic integration formulasFormulaIn A.1. Basic integration formulasFormulaCopy LaTeX∫duu=ln∣u∣+C\int \frac{du}{u} = \ln|u| + C∫udu=ln∣u∣+CTagsA 1 formulas basic of integrationDifferential calculusDerivativeDerivative formulaTableVariablesCCCConstante real de integraciónuuuVariable auxiliar de sustitucióndududuDiferencial respecto de uuuln\lnlnNatural logarithmFound an error? Contact us.Related formulasRelatedFormula∫dxx=ln∣x∣+C\int \frac{dx}{x}=\ln|x|+C∫xdx=ln∣x∣+COpen formulaOpen in sectionRelatedA.1.2 Power rule and elementary functions∫un du=1n+1 un+1+C,n≠−1\int u^n\,du = \frac{1}{n+1}\,u^{n+1} + C, \quad n \neq -1∫undu=n+11un+1+C,n=−1Open formulaOpen in sectionRelatedFormula∫eu du=eu+C\int e^u\,du = e^u + C∫eudu=eu+COpen formulaOpen in sectionRelatedFormula∫au du=aulna+C,a>0, a≠1\int a^u\,du = \frac{a^u}{\ln a} + C, \qquad a>0,\ a\neq1∫audu=lnaau+C,a>0, a=1Open formulaOpen in sectionRelatedA.1.3 Basic trigonometric integrals∫sin u du=−cosu+C\int \sin\,u\,du = -\cos u + C∫sinudu=−cosu+COpen formulaOpen in sectionRelatedFormula∫cosu du=sin u+C\int \cos u\,du = \sin\,u + C∫cosudu=sinu+COpen formulaOpen in sectionRelatedFormula∫sec2u du=tanu+C\int \sec^2 u\,du = \tan u + C∫sec2udu=tanu+COpen formulaOpen in sectionRelatedFormula∫csc2u du=−cotu+C\int \csc^2 u\,du = -\cot u + C∫csc2udu=−cotu+COpen formulaOpen in section