Subjects/Calculus II/A.2. Trigonometric integrals/A.2.3 Reduction formulasA.2. Trigonometric integralsA.2.3 Reduction formulasIn A.2. Trigonometric integralsFormulaCopy LaTeX∫sinnudu=−n1sinn−1ucosu+nn−1∫sinn−2uduVariablesuVariable auxiliar de sustituciónnExponente o índice enteroduDiferencial respecto de uRelated formulasRelatedFormula∫csc3udu=−21cscucotu+21ln∣cscu−cotu∣+COpen formulaOpen in sectionRelatedFormula∫cosnudu=n1cosn−1usinu+nn−1∫cosn−2uduOpen formulaOpen in sectionRelatedFormula∫sec3udu=21secutanu+21ln∣secu+tanu∣+COpen formulaOpen in sectionRelatedFormula∫tannudu=n−11tann−1u−∫tann−2uduOpen formulaOpen in sectionRelatedFormula∫cot3udu=−21cot2u−ln∣sinu∣+COpen formulaOpen in sectionRelatedFormula∫tan3udu=21tan2u+ln∣cosu∣+COpen formulaOpen in sectionRelatedFormula∫cos3udu=31(2+cos2u)sinu+COpen formulaOpen in sectionRelatedA.2.2 Odd powers (n=3)∫sin3udu=−31(2+sin2u)cosu+COpen formulaOpen in section