techniques of integration

eliminating square root
1. use trigo identity, and refer graph
3. use when have trigo f(x) in square root, and when trigo f(x) can be simplified
improper integral
1. when
2. when denominator can be undefined
basic substitution method
1. general exponential f(x)
2. natural log
3. hyperbolic f(x)
  1. linear f(x)
    1. integrate
  2. not linear f(x)
    1. use substitution method, then integrate
4. inverse trigo f(x)
  2. stewart's table
5. exponential f(x)
  2. get in exponential, then integrate
6. trigo f(x)
  1. indefinite
  2. definite
7. inverse hyperbolic f(x)
trigonometric integrals
1. power(even), use half angle formula
2. both power(odd), factorize the smallest power
3. power 1, use identities
4. power is too big, use reduction formula
5. both power(even), use half angle formula
6. power(odd), factorize until either one got power 1
7. power(odd&even), factorize the odd power
by parts
1. when cannot use subs method
2. choose u & dv
  1. 1. integrate dv
    2. differentiate u (ILATE)
4. tabular integration
  1. stop when last eq = ques
  2. when differentiate u=0
    1. differentiate until get 0, integrate dv, make arrow
  3. when differentiate u never get 0
partial fraction
1. non repeated linear factors
  2. heaviside 'coverup' method, factorize lowest degree, integrate
2. repeated linear factors
  1. when denominator repeated
  2. find v- by comparing the coefficient
3. improper fraction
  1. use long division method, heaviside method, integrate
4. irreducible quad factors
  1. when quad factor cannot be factorize
  3. heaviside method, integrate
trigo substitution
trigonometric identities
1. use when have summation of two terms power two, and when have different angle
2. expand first, then apply trigo identity
improper fraction
1. when numerator > denominator
2. how?
  1. long division method, integrate
separating fractions
1. use substitution method, then integrate
2. use when fraction can be separated, and result to a simpler intergrand
completing the square
1. use when no substitution available and when have quadratic f(x) at denominator
3. use completing the square, then integrate
multiplying by form of 1
1. use when the equation is in 1 term
2. how?
  1. conjungate , identity, separate, integrate

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techniques of integration

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