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  3. Chapter 3 - Techniques of Integr...
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  5. Algebraic Substitution | Integration by Substitution

Algebraic Substitution | Integration by Substitution

In algebraic substitution we replace the variable of integration by a function of a new variable. A change in the variable on integration often reduces an integrand to an easier integrable form.
 

$$ \int f(g(x)) \, g'(x) \, dx = \int f(u) \, du $$

where $u = g(x)$
 

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  • Problem 1: Evaluate $\displaystyle \int \dfrac{(8x + 1) \, dx}{\sqrt{4x - 3}}$ by Algebraic Substitution
  • Problem 2: Evaluate $\displaystyle \int y^3\sqrt{2y^2 + 1} \,\, dy$ by Algebraic Substitution
  • Problem 3: Evaluate $\displaystyle \int \dfrac{x^3 \, dx}{(x^2 + 1)^3}$ by Algebraic Substitution
  • Problem 4: Evaluate $\displaystyle \int \dfrac{y \, dy}{\sqrt[4]{1 + 2y}}$ by Algebraic Substitution
  • Problem 5: Evaluate $\displaystyle \int \dfrac{(6z - 1) \, dz}{\sqrt{(2z + 1)^3}}$ by Algebraic Substitution

Book traversal links for Algebraic Substitution | Integration by Substitution

  • Integration by Substitution | Techniques of Integration
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  • Problem 1: Evaluate $\displaystyle \int \dfrac{(8x + 1) \, dx}{\sqrt{4x - 3}}$ by Algebraic Substitution

Navigation

  • Chapter 1 - Fundamental Theorems of Calculus
  • Chapter 2 - Fundamental Integration Formulas
  • Chapter 3 - Techniques of Integration
    • Integration by Parts | Techniques of Integration
    • Integration by Substitution | Techniques of Integration
      • Algebraic Substitution | Integration by Substitution
        • Problem 1: Evaluate $\displaystyle \int \dfrac{(8x + 1) \, dx}{\sqrt{4x - 3}}$ by Algebraic Substitution
        • Problem 2: Evaluate $\displaystyle \int y^3\sqrt{2y^2 + 1} \,\, dy$ by Algebraic Substitution
        • Problem 3: Evaluate $\displaystyle \int \dfrac{x^3 \, dx}{(x^2 + 1)^3}$ by Algebraic Substitution
        • Problem 4: Evaluate $\displaystyle \int \dfrac{y \, dy}{\sqrt[4]{1 + 2y}}$ by Algebraic Substitution
        • Problem 5: Evaluate $\displaystyle \int \dfrac{(6z - 1) \, dz}{\sqrt{(2z + 1)^3}}$ by Algebraic Substitution
      • Trigonometric Substitution | Techniques of Integration
    • Integration of Rational Fractions | Techniques of Integration
  • Chapter 4 - Applications of Integration

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