Strategy for Integration

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Section 8.5

• Strategy for Integration

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HINT1
Simplify the integrand if possible.
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HINT 2
Look for an obvious u-substitution.
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HINT 3
Classify the integrand according to form.

• Trigonometric Functions Use the techniques of
  Section 8.2
• Rational Functions Use the technique of Partial
  Fractions (Section 8.4).
• Integration by Parts Try Integration by Parts
  if there are two functions multiplied.
• Radicals
• Square roots with radicand of the form x2 a2
  require trigonometric substitution (Section 8.3)
• nth root with a radicand of the form ax b can
  usually be solved by using the rationalizing
  substitution

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HINT 4
Try again.

• Try substitution. Some substitutions are not
  obvious.
• Try parts even if the problem does not look like
  parts will work. It may work.
• Manipulate the integrand. Many times this
  involves multiplying the numerator and
  denominator by the same term.
• Try to relate the problem to previous problems.
• Use several integration techniques in the same
  problem.