Calculate each of the definite integrals in Exercises 47–52. Some integrals require partial fractions or polynomial long division, and some do not. 4 dr x² – 4 4(x² – 1) dx x² – 4 47. 48. 3. 1 1 dx x(х + 1) dx x' (x + 1) 49. 50. x² – 2x – 4 dx 1 dx x(х + 2)(х — 3) 51. 52. х — 3

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Q: 1. Evaluate the integral by partial fraction decomposition technique: 3x² – x + 1 -dx. x³ – x² -

A: Method:- Need to use partial fraction decomposition technique to evaluate integral

Q: In Exercises 1–8, decide whether the integral is improper. Explain your reasoning. dx dx 1. 5х — 3 -…

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Q: х —9 Evaluate the integral using partial fraction decomposition: | Jx+5)(x– 2)

A: Given∫x-9(x+5)(x-2)dx

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Q: dx -dx x* +х — 2 9.

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A: In the question we need to evaluate the integral.

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A: Given that

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A: take long division

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A: Given problem:-

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A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 5) (a) Show that F = (8-14xy2 + 2ye²x) + (e²x - 14x²y) y is conservative. (b) Find a potential…

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Q: 1) Evaluate each integral by substitution: (In x) dx a)f(x+1)(x +2x)'dx b)fxVx² +9dx 「ズ dx 7x+5 dx…

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Q: Activity 2: Use partial fractions to compute each integral. Must work the integrals out by hand and…

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Q: Use partial fractions to evaluate the definite integral. ∫12 (x+1)/x(x2+1)dx

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Q: Evaluate the integral. 7 √49-x² √49-x²-22 49-x² 1 √²-3³ (x² + y² + 2²)1/2 dy dz dx =

A: Solution:-

Q: In general, a partial fractions integral with a repeated irreducible quadratic factor will result in…

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Q: x² +x – 2 -dx 3x – x² + 3.x – 1 10.:

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Q: EXERCISES 7.3 Evaluate these definite integrals. dx Vx+2 1. -5 dx Vx – 1 2. 3. 3x²e*³dx

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Q: Step by step

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Q: Evaluate the integral. 5n /2 2, 1 - cos t dt 3π/2

A: ∫3π25π21-cos2tdt=∫3π25π2sin2tdt=∫3π25π2sintdt=∫3π22π-sintdt+∫2π5π2sintdt=1+1=2

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Q: 10. Find the integral of dx x²-4 O In() + C x-2 O In() + C 2x x+2 O fIn( *2) + C X+2 O In() + C x+2…

A: *using concept:- 1. Partial fraction. 2. int(dx/x) = ln(x). 3. ln(m) - ln(n) = ln(m/n).

Q: Use Partial Fraction Decomposition to evaluate the following integrals.

A: To find the integration by partial fraction

Q: Evaluate the integral. x² - 81 | V=² x x² - 81 | Vx² x √x². 81 X √x². 81 X x² - 81 X 1² 1² - dx = -…

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Q: 1. Use integration by parts to find the integral below. In(x19)– 9x10+C a. b. x ·In(x1)– 10x10+ C c.…

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Q: Apply u- substitution and the partial fraction decomposition to evaluate the integral In(x² + x + 1)…

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A: First divide and then integrate

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Q: 3-Evaluate the integrals in Exercises: 2√3 So dx √4 + 4 + x² 0 4- 6 dx 5. Sot v Jo V1 + 9x² cos x dx…

A: We have to evaluate the integrals.

Q: 6. Evaluate the integral by partial fractions decomposition. 3x3 + 1 dx x3 - x2 +x - 1

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Q: Find the integration inner product on C[-4, 3] of the given functions. f(x) = 16x g(x) = 2x?

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Q: Compute the given integral. Using Partial Fraction Method 9х-21 dx = x2-4x-5

A: To solve the given Integral using partial fraction  ∫ (9x -21)/ (x2- 4x -5) dx

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A: Given integral is: I=∫4x4+12x3+x2-xdx Integrating it by using partial fraction decomposition:…

Q: 6. Evaluate the integral by partial fractions decomposition. Зx3 + 1 dx x3 – x² + x – 1

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Q: 1) By partial fraction , compute the following integrals x' +x 1. x-1 Зх +5 2. ' (x +1)(x-1)*"

A: Since you have asked multiple questions, we will solve the first question for you ∫x3+xx-1dx take…

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Q: Use the integration theorem to show that Cos nx 효(72-3a2) =D Σ(-1)”-1! -T <x < T n2 n=1 and sin nx…

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Q: (6) Find the indefinite integral - 3x+2 x+1 12x-22x dx (O) 3x -11x +15 x' +2x +3 dx (c)+3x +9x x In…

A: Solution is given as below: