Methods of Integration

1) Basic Integration rules

  • Power Rule

  • Constant multiple rule - factor out constants

2) Integration by Substitution (U-Sub)

3) Integration by Parts

4) Partial Fraction Decomposition

5) Integration of Inverse Trig

6) Integration using long division of polynomials

  • The degree of the numerator is greater than or equal to the denominator —> perform long division

  • Usually results in an ln function after integration

7) Integration of e^x

8) Integration of regular Trig Functions

Test 2/28/25

  • Methods of Integration

  • Arc Length

    • ab(1+[f’(x)]2dx for equation f(x)

    • If asking to find the perimeter of an area enclosed by 2 equations f(x) and g(x)

      • ab(1+[f’(x)]2+(1+[g’(x)]2dx

  • Remember: Derivatives of ln, e^x, and trig

Derivatives of Trig

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