About Reduction Formula
In integration, a reduction formula is frequently used to calculate higher-order integrals. Working with higher degree expressions is time-consuming and tiresome, hence the reduction formulae are supplied as simple expressions with a degree of n to answer these higher degree expressions. These reduction formulae are generated from the integration base formulas and follow the same integration rules.
following reduction formulas can be used to work with algebraic variables, trigonometric functions, and logarithmic functions in higher-degree expressions. The reduction formulas are presented as four separate formulas below.
Formula 1
Basic exponential expressions reduction formula.
∫xn.emx.dx=1/m.xn.emx − n/m∫xn−1.emx.dx
Formula 2
Reduction Formula for the logarithmic expressions.
- ∫lognx.dx=xlognx−n∫logn−1x.dx
- ∫xnlogmx.dx=xn+1logmx / n+1 − m/n+1 ∫xnlogm−1x.dx
Formula 3
Reduction Formula for the trigonometric functions.
- ∫Sinnx.dx= −1/n Sinn−1x.Cosx+ n−1/ n ∫Sinn−2x.dx
- ∫Cosnx.dx = 1/n Cosn−1x.Sinx + n−1/ n ∫Cosn−2 x.dx
- ∫Sinnx.Cosmx.dx = Sinn+1x.Cosm−1x /n+m + m−1/n+m ∫Sinnx.Cosm−2x.dx
- ∫Tannx.dx= 1/n−1 .Tann−1 x − ∫Tann−2 x.dx
Formula 4
Reduction Formula for algebraic expressions.
∫ xn/axn+b .dx = x/a − b/a ∫ 1/axn+b .dx
∫lognx.dx = xlognx - n∫logn-1x.dx
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