Home/Calculus II/Typical reduction formulas/Formula5.3. Typical reduction formulasFormulaIn 5.3. Typical reduction formulasFormulaCopy LaTeX∫cotnx dx=−cotn−1xn−1−∫cotn−2x dx,n>1\int \cot^n x\,dx =-\frac{\cot^{n-1}x}{n-1}-\int\cot^{n-2}x\,dx, \qquad n>1∫cotnxdx=−n−1cotn−1x−∫cotn−2xdx,n>1Tagsantiderivativeintegration by parts: reduction formulasby partsreductiontecnica fundamentalVariablesxxxVariable independiente (variable de integración)nnnExponente o índice enterodxdxdxDiferencial respecto de xxxConditionsn>1n>1n>1Found an error? Contact us.Related formulasRelatedFormula∫tannx dx=tann−1xn−1−∫tann−2x dx,n>1\int \tan^n x\,dx =\frac{\tan^{n-1}x}{n-1}-\int\tan^{n-2}x\,dx, \qquad n>1∫tannxdx=n−1tann−1x−∫tann−2xdx,n>1Open formulaOpen in sectionRelatedFormula∫secnx dx=secn−2xtanxn−1+n−2n−1∫secn−2x dx,n>1\int \sec^n x\,dx =\frac{\sec^{n-2}x\tan x}{n-1} +\frac{n-2}{n-1}\int\sec^{n-2}x\,dx, \qquad n>1∫secnxdx=n−1secn−2xtanx+n−1n−2∫secn−2xdx,n>1Open formulaOpen in sectionRelatedFormula∫cosnx dx=cosn−1xsinxn+n−1n∫cosn−2x dx,n≥2\int \cos^n x\,dx =\frac{\cos^{n-1}x\sin x}{n} +\frac{n-1}{n}\int\cos^{n-2}x\,dx, \qquad n\ge2∫cosnxdx=ncosn−1xsinx+nn−1∫cosn−2xdx,n≥2Open formulaOpen in sectionRelatedFormula∫cscnx dx=−cscn−2xcotxn−1+n−2n−1∫cscn−2x dx,n>1\int \csc^n x\,dx =-\frac{\csc^{n-2}x\cot x}{n-1} +\frac{n-2}{n-1}\int\csc^{n-2}x\,dx, \qquad n>1∫cscnxdx=−n−1cscn−2xcotx+n−1n−2∫cscn−2xdx,n>1Open formulaOpen in sectionRelatedFormula∫sinnx dx=−sinn−1xcosxn+n−1n∫sinn−2x dx,n≥2\int \sin^n x\,dx =-\frac{\sin^{n-1}x\cos x}{n} +\frac{n-1}{n}\int\sin^{n-2}x\,dx, \qquad n\ge2∫sinnxdx=−nsinn−1xcosx+nn−1∫sinn−2xdx,n≥2Open formulaOpen in sectionRelatedFormula∫xneax dx=xneaxa−na∫xn−1eax dx,a≠0\int x^n e^{ax}\,dx =\frac{x^n e^{ax}}{a}-\frac{n}{a}\int x^{n-1}e^{ax}\,dx, \qquad a\neq0∫xneaxdx=axneax−an∫xn−1eaxdx,a=0Open formulaOpen in section