Home/Calculus II/A.1. Basic integration formulas/FormulaA.1. Basic integration formulasFormulaIn A.1. Basic integration formulasFormulaCopy LaTeX∫secu du=ln∣secu+tanu∣+C\int \sec u\,du = \ln|\sec u + \tan u| + C∫secudu=ln∣secu+tanu∣+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∫cotu du=ln∣sin u∣+C\int \cot u\,du = \ln|\sin\,u| + C∫cotudu=ln∣sinu∣+COpen formulaOpen in sectionRelatedFormula∫cscu du=ln∣cscu−cotu∣+C\int \csc u\,du = \ln|\csc u - \cot u| + C∫cscudu=ln∣cscu−cotu∣+COpen formulaOpen in sectionRelatedA.1.4 Trigonometric integrals (logarithmic forms)∫tanu du=−ln∣cosu∣+C\int \tan u\,du = -\ln|\cos u| + C∫tanudu=−ln∣cosu∣+COpen formulaOpen in sectionRelatedA.1.5 Integrals yielding inverse trigonometric functions∫dua2−u2=arcsinua+C\int \frac{du}{\sqrt{a^2 - u^2}} = \arcsin\frac{u}{a} + C∫a2−u2du=arcsinau+COpen formulaOpen in sectionRelatedFormula∫cscu cotu du=−cscu+C\int \csc u\,\cot u\,du = -\csc u + C∫cscucotudu=−cscu+COpen formulaOpen in sectionRelatedFormula∫dua2+u2=1a arctanua+C\int \frac{du}{a^2 + u^2} = \frac{1}{a}\,\arctan\frac{u}{a} + C∫a2+u2du=a1arctanau+COpen formulaOpen in sectionRelatedFormula∫secu tanu du=secu+C\int \sec u\,\tan u\,du = \sec u + C∫secutanudu=secu+COpen formulaOpen in sectionRelatedFormula∫duuu2−a2=1a arcsec∣ua∣+C\int \frac{du}{u\sqrt{u^2 - a^2}} = \frac{1}{a}\,\operatorname{arcsec}\left|\frac{u}{a}\right| + C∫uu2−a2du=a1arcsecau+COpen formulaOpen in section