sec7_1

# sec7_1 - ± xe x dx Example 3.2 ± x 2 cos x dx Example 3.3...

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7.1 Integration by Parts 1. Introduction Recall from Calculus I Example 1.1. ± xdx Example 1.2. ± e x dx = Example 1.3. ± xe x dx = Now recall the product formula: d dx [ f ( x ) g ( x )] = Or written another way: d dx ( uv )= 1

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Section 7.1 2 2. Integration by Parts Formula Theorem 2.1. ± f ( x ) g ± ( x ) dx = or ± udv = Remark 2.1. When choosing dv choose something whose integral is simple. When choosing u , choose something that will become simpler when it is diﬀerentiated (if possible). 3. Examples Example 3.1.

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Unformatted text preview: ± xe x dx Example 3.2. ± x 2 cos x dx Example 3.3. ± tan-1 2 x dx Example 3.4. ± x sec 2 x dx Section 7.1 3 Example 3.5. ± π/ 2 x 2 sin 2 x dx Example 3.6. ± 1 / 2 cos-1 x dx Example 3.7. ± 1 x 3 √ 4 + x 2 dx Example 3.8. ± ln x dx Section 7.1 4 4. Reduction Formulas Example 4.1. for sine (Example 6 in text) ± sin n x dx =? Example 4.2. Find ± sin 4 x dx...
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sec7_1 - ± xe x dx Example 3.2 ± x 2 cos x dx Example 3.3...

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