Consider the integral dx then (which statement(s) is/are correct) 2 -4X 1 (1) z In(x-4)-Inx]+C when using partial fractions (i) x -4x 4 (ii) x – 4x 1 1 dx =tanh 2 -1 (x-2) -1 +C when completing the square 2

Q: ТР-4 Evaluate the integral below with consideration of the concept of substitution leading to…

A: To evaluate I=∫1xx+112dx...(1)

Q: Evaluate the integral using the method of partial fractions. x-9 -dx (x+5)(x-2)

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Q: Consider S x-m+ (A) 6 B) 5 3x5 3x4+6x³3x² - 6x A B C + + x-1 x+1 x+m 17/6 (D) 14/3 -dx. Using the…

A: Here is the solution of the given problem. Method of Partial Decomposition

Q: Consider ·S= x-m+- Sx 3x5 -dx. Using the method of partial fractions, the given integral can be…

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Q: Consider and C. -dx Using the method of partial fractions, the given integral can be written as…

A: Here, 3x53x4+6x3-3x2-6x=x-m+Ax-1+Bx+1+Cx+mor, x4x3+2x2-x-2=x-m+Ax-1+Bx+1+Cx+mor,…

Q: I+116 Jz- 10)(z+9) dz, by expressing the integrand as the sum of the partial fractions. Evaluate

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Q: 9. Evaluate the integral by using partial fractions decomposition. 7 dx x3 – 8x + 23x

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Q: 9. Evaluate the integral by using partial fractions decomposition. 7 dx x3 – 8x² + 23x

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Q: Use the method of partial fractions to evaluate each of the following integral. dx Jalx – 1)(x –…

A: The given integral is: I=∫dxx(x-1)(x-2)(x-3)

Q: Express the integrand as a sum of partial fractions and evaluate the integral. 16x S dx (x- 21)(x+…

A: Explained below

Q: x + 174 Evaluate dx, by expressing (x – 8)(x + 9) the integrand as the sum of the partial fractions.

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Q: Using the method of partial fractions, compute the indefinite integral dx. 3x – 2x2 – 1

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Q: dx -dx x* +х — 2 9.

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Q: x + 117 dx, by J Ta – 6)(x + 9) Evaluate - expressing the integrand as the sum of the partial…

A: Evaluate the given expression.  We are solving this problem using the partial fractions.

Q: бх+2 J x²-3x-28 Write the form of the partial fraction, and then evaluate the integral,

A: To find: ∫6x+2x2-3x-28dx

Q: Consider the indefinite integral [8.2³ 18x³ + 7x² + 3x + 4 -dx x¹ + 1x² Then the integrand has…

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Q: Consider f(x-m+ A) 14/3 B) 5 C) 6 D) 17/6 ·S= 3x5 3x4+6x33x2 - 6x B C + x-1 x+1 x+m A x-m+ + -dx.…

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Q: Consider the indefinite integral r8x³ + 7x² + 45x + 36 dx x4 + 9x2 Then the integrand has partial…

A: Consider the indefinite integral ∫8x3+7x2+45x+36x4+9x2 dxThen the integrand has partial fractions…

Q: Express the integrand as a sum of partial fractions and evaluate the integral. 5x3 + 18x2 + 43x + 13…

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Q: Integrate the following using Partial Fractions. 1. S a dz r2-3x-4

A: Solving the problem by finding the integration.

Q: Evaluate the integral using Partial Fraction Decomposition. t3 +t -1 dt t4 + 2t2 + 1

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Q: Q3) Find the integration by using Partial fraction method Y x² + 2x + 1 (x² + 1)² dx

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Q: 12 By using partial fractions, show t 1 x² -1 2(x+1) 2(x–1)' Hence, evaluate dx

A: We have to solve the integral

Q: Consider x-m+ A 17/6 B 14/3 с 6 3x5 3x4+6x3 3x2 - 6x A B C + + x-1 x+1 x+m -dx. Using the method of…

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Q: Consider the following indefinite integral. 9x3 + 5x2 + 36x + 27 dx x4 + 9x2 The integrand has…

A: Concept used-Partial fraction method of integration

Q: (c) Considering, 4x x² + 9x + 8 (i) Separate it into partial fractions. (ii) Hence, find 4х -dx J x²…

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

A: To find the integration by partial fraction

Q: 3x + x-10 OHence, evaluate dx by first expressing the integrand as sum of partial x2 +4x+4…

A: Explanation of the answer is as follows

Q: Evaluate the integral using Partial Fraction Decomposition. Зx4 — Зх?k? + Зх3 — k?x — 2kx? dx - - х4…

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Q: Consider s √(x- x-m+ 06 05 O 17/6 14/3 3x5 3x4+6x3-3x2 - 6x A B C + + x-1 x+1 x+m dx Using the…

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Q: Consider √(x- ·S= x-m+ 3x5 3x4+6x³-3x² - 6x A B C + + x-1 x+1 x+m A) 5 B) 6 C) 17/6 14/3 -dx. Using…

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

A: Given

Q: 7. Consider the indefinite integral J Then the integrand has partial fractions decomposition…

A: Given problem:-

Q: Consider the indefinite integral (7x³ +6x2 + 3x + 3 -dx x4 + lx? Then the integrand has partial…

A: The given integral: ∫7x3+6x2+3x+3x4+1x2dx

Q: Find the partial integral. gy Y dx /1

A: y will behave as constant

Q: х* — 5х3 +6х? —18 dx, x' – 3x?

A: First divide and then integrate

Q: 3x+1 Evaluate the integral -dx by the method of Partial Fractions. x² +3x+2

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Q: Q#3: a) Evaluate the following integralS sec®x dx by using the reduction formula of cosine. b)…

A: Question no. 3a,Given,           ∫sec8xdx

Q: (e ) Find the f(sin g + cotq - eseti + q5) dq (d)Using the method of Partial fractions find / 2x+5…

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Q: 2х + 3 Using partial fractions, the integral x(x² + 2x + 5) – (x² + 2x + 5) dx - A Вх + С can be…

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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

Q: Hence find the particular integral and the general solution in the form 2. Express f(x) in partial…

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

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Q: 6. Use integration by partial fractions to integrate the following, show detailed solution b) -dx…

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Q: 1 Express the integrand as a sum of partial fractions and evaluate the integral dx. (x-1) (x²+1)

A: Break into partial sum then integrate

Q: (x²-2x+3)dx 2. J (x-1)(x² + 4x + 4)

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Q: 5x° + 8x2 + 48x + 96 x4 + 16x? Then the integrand has partial fractions decomposition Consider the…

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