Maths Volume-8 Part I(Indefinite Integral)



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Contents

Standard Forms of Integration - I


Description: Standard forms of integration involve recognizing common integral patterns for efficient problem-solving.


Standard Forms of Integration - II


Description: Integration formulas simplify calculations by directly applying predefined integral results to functions.


Standard Forms of Integration - III


Description: Common integral forms help evaluate functions involving trigonometric, logarithmic, and exponential expressions easily.


Problems on Basic Substitution - I


Description: Basic substitution method replaces variables to simplify and solve complex integrals efficiently.


Problems on Basic Substitution - II


Description: Recognizing suitable substitutions helps transform integrals into standard forms for easy evaluation.


Problems on Basic Substitution - III


Description: Proper substitution simplifies expressions, reducing complex integrals into manageable standard forms.


Integration by Parts - I


Description: Integration by parts applies the product rule in reverse to integrate products of functions.


Integration by Parts - II


Description: Choosing appropriate functions for differentiation and integration is crucial in integration by parts.


Integration by Parts - III


Description: Repeated application of integration by parts helps evaluate complex integrals systematically.


Integration by Parts - IV


Description: Using tabular integration speeds up repeated applications of integration by parts in long expressions.


Integration by Parts - V


Description: Complex integrals often require a strategic combination of integration by parts and substitution methods.


Some Special Substitutions and Integrals - I


Description: Special substitutions handle integrals involving square roots, trigonometric identities, and rational expressions.


Some Special Substitutions and Integrals - II


Description: Transforming variables using special substitutions simplifies otherwise difficult integral expressions.


Some Special Substitutions and Integrals - III


Description: Recognizing patterns in special integrals aids in selecting the best substitution method for solving.


Synopsis of Indefinite Integral - III


Description: Basic integration techniques include substitution, partial fractions, and algebraic manipulation for solving integrals.


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