Reduction Formulas for Logarithmic Functions

For logarithmic functions, reduction formulas are:

  • ∫ lognx dx = xlognx -n∫logn-1x dx
  • ∫xnlogmx dx = xn+1logmx/ (n+1) – {(m)/(n+1)}.∫xnlogm-1x dx

Reduction Formula

Reduction formula in mathematics is generally used for solving integration of higher order. Integration involving higher-order terms is difficult to handle and solve. So, to simplify the solving process of higher-order terms and get rid of the lengthy expression-solving process of higher-order degree terms – Integration processes can be simplified by using Reduction Formulas.

Table of Content

  • What is Reduction Formula?
  • Reduction Formulas for Logarithmic Functions
  • Reduction Formulas for Algebraic Functions
  • Reduction Formulas for Trigonometric Functions
  • Reduction Formulas for Exponential Functions
  • Reduction Formulas for Inverse Trigonometric Functions
  • Examples Using Reduction Formula
  • FAQs on Reduction Formula

Similar Reads

What is Reduction Formula?

Reduction formulas are used to simplify the higher-order terms. Integration of higher-order terms consisting of logarithmic, algebraic, and trigonometric functions are simplified by reduction formulas. In the Reduction formula, higher-order degree terms are given a degree n. Reduction formulas with degree n are derived from the integration base formulas. All rules of integration apply to these reduction formulas as well....

Reduction Formulas for Logarithmic Functions

For logarithmic functions, reduction formulas are:...

Reduction Formulas for Algebraic Functions

For algebraic functions, reduction formulas are:...

Reduction Formulas for Trigonometric Functions

For trigonometric functions, reduction formulas are:...

Reduction Formulas for Exponential Functions

For exponential functions, reduction formulas are:...

Reduction Formulas for Inverse Trigonometric Functions

For inverse trigonometric functions, reduction formulas are:...

Examples Using Reduction Formula

Example 1: Simplify ∫ x2.log2x dx...

FAQs on Reduction Formula

What Is a Reduction Formula?...