Use the method of partial fractions to evaluate the following integral. ∫((x^2) − x + 2/(x − 1)((x^2) + x + 1)   dx

Q: Use any method to evaluate the integrals

A: Since you have posted multiple question we solve first question for you  To get the solution of…

Q: Evaluate the following Integrals using Integration by Partial Fraction. Show all the solution.

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Q: Evaluate the integral from -1 to 0 using partial fractions: ∫(x3-4x+1) / (x2-3x+2) dx

A: Here we use partial fraction: ∫1(x-a)(x-b) dx=A(x-a)+B(x-b)

Q: x³ + 4 dx x (x+1)

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Q: 1 dx 1 – x?

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Q: to de 4

A: For    kx2 - a2  we can use substitution kx = asecθ . Then use trigonometric identity to simplify it…

Q: Use any method to evaluate the integral. dx X>11 (x²-121) 3/2

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Q: 2 x ln((2x)²) dx 1

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Q: Evaluate the integral: / (3x+5)dx x²+2x+1

A: ..............(1)

Q: Evaluate the integral by integration by partial fractions

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Q: x³ + 12 dx. x² + 6x + 8

A: Please see the explanation below

Q: x*+2х+3

A: We can find the integration as below.

Q: Evaluate the integral V212 -7x2 dx 1 – x²

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Q: Evaluate the integrals using partial fraction 3y²-y+! S y³ - y² dy

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Q: Evaluate the integral. integral   x 4  + 3x 2 +1      /  x 5 +5 x 3 +5x  dx

A: Given: ∫x4+3x2+1x5+5x3+5xdx for evaluating given integral we substitute x5+5x3+5x=t now…

Q: Consider the indefinite integral (4x³ + 5x² − 1x − 6 [420³ + x² - 1 dx

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Q: Use any method to evaluate the integrals ∫ x3 - 2x2 - 3x/x + 2 dx

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Q: 5T 2x 2x. - sinº Scos ()dx 4

A: First reduced the integrand function into single function by using trigonometrical identity and then…

Q: x – 6 dx = (x + 8)(x + 5)²

A: The integral is  ∫x-6x+8x+52dx By using the partial fraction,…

Q: Find the indefinite integral. x² + 4x +3 dx x3 + 6x2 + 9x + 8

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Q: dx ¤(x+2)²

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Q: valuate the integral using Partial Fraction Technique: 7- 5) (x – 9)2 dx

A: To evaluate: ∫xx-5x-92dx. Simplifying the expressio using partial fraction decomposition.…

Q: Use any method to evaluate the integral. x°dx Vx + 144

A: To Evaluate:

Q: dx 1+x3

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Q: dx

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Q: dx 21 VI(Vx + 1)'

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Q: 4 dx 7). S x4-1

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Q: evaluate the integrals 5x^3/1+x^8 dx

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Q: Evaluate the integral x³ /x² +6 dx. X + 6 dx. .3 x +6 dx =

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Q: Evaluate the integrals: 1. 2. -2 dx 0 8+2x² x+3 2x3-8x S - dx

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Q: Use partial fractions to find the indefinite integral. integral((x^2-x)/(x^2+x+1))dx

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Q: х — 3 х3 -4х

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Q: Use any method to evaluate the integral. 3 x*dx 2 Vx + 25 3 x*dx S- 2 Vx +25

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Q: 2x – x3 1. Evaluate dx. (r – 1)²(x²+1). -

A: we want to find the value of the given integral I=∫2x-x3(x-1)2(x2+1) dx

Q: Find the integral (4x2 – 21x) dx (x – 3) (2x + 3)

A: The partial fraction decomposition or partial fraction expansion of a rational fraction is an…

Q: Use partial fractions to find the indefinite integral ∫ 5 / (x2 + 3x − 4)   dx

A: Evaluate: ∫5x2+3x-4 dx

Q: 2x – 5 dx x(x – 1)3

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Q: Find the indefinite integral. x² + 4x + 3 dx x3 + 6x2 + 9x + 8

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Q: x(4+ x²)!/3 dx

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Q: 1 S dx 1+x3

A: First we take partial fraction.

Q: Evaluate the integral. integral       x +4 / (x  2 + 2  x  + 5 ) dx

A: The given integral ∫x+4x2+2x+5dx can be evaluated as, ∫x+4x2+2x+5dx=∫x+4x+12+22dx…

Q: Find the indefinite integral ∫ (x2 + 2x + 3) / (x3 + 3x2 + 9x)   dx

A: To evaluate ∫x2+2x+3x3+3x2+9xdx

Q: Find the indefinite integral. x2 + 4x + 3 dx x³ + 6x2 + 9x + 6

A: Here we have to solve integral equation by substitution.

Q: 2Evaluate the improper integral X+2 dx 3x²412X

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Q: 32. ³+x²+x+2 + 1)(x² + 2) dx

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Q: (3x-3) dx (x²-2x+1)(x²+2x+8)

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Q: Use any method to evaluate the integral. x'dx 2 X + 16

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Q: 4x2 – 1 -dx. J 3(3x + 1)

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Q: Evaluate the integral using integration by parts rule if [x cos 2x dx 5) Express the integrands as a…

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Q: 2x +4 dx x* +4 4

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