13th - x Problem . Evaluate, if possible, the following...

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Partial fractions, improper integrals David Pierce December  ,  Problem . Compute the following indefinite integrals. (a) Z x 3 - x x 2 - x - 6 d x (b) Z x x 2 + x + 1 d x (c) Z x ( x 2 + x + 1) 2 d x (d) Z x 4 - 3 x 3 + 4 x 2 - 3 x + 1 x 4 + 3 x 3 + 4 x 2 + 3 x + 1 d x (e) Z 4 x 3 + 9 x 2 + 8 x + 3 x 4 + 3 x 3 + 4 x 2 + 3 x + 1 d x Problem . Assuming deg f < 8 , analyse f ( x ) ( x 2 + 4 x - 5) 2 · ( x 2 + 4 x + 5) 2 as a sum of partial fractions. (No need to compute the numerators.) Problem . Evaluate the following definite integrals. (a) Z 32 0 d x 1 + x 1 / 5 (b) Z π / 2 0 d x 2 + sin
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Unformatted text preview: x Problem . Evaluate, if possible, the following improper integrals. (a) Z 1-1 d x x 3 (b) Z ∞-∞ d x x 3 · e 1 /x 2 (c) Z ∞-∞ d x | x 3 | · e 1 /x 2 Problem . Determine whether the following improper integrals converge. (a) Z ∞ sin( x 3 ) x + e x d x (b) Z ∞ 2 d x x 2-x-2 (c) Z ∞ 1 d x x 2-x-2...
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