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Section 8.5

Section 8.5. Strategy for Integration. HINT1. Simplify the integrand if possible. HINT 2. Look for an obvious u -substitution. HINT 3. Classify the integrand according to form. Trigonometric Functions : Use the techniques of Section 8.2

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Section 8.5

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  1. Section 8.5 Strategy for Integration

  2. HINT1 Simplify the integrand if possible.

  3. HINT 2 Look for an obvious u-substitution.

  4. 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

  5. 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.

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