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

  • ∫_a^b√(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)

    • ∫_a^b√(1+[f’(x)]²+√(1+[g’(x)]²dx

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