1) Create your rational function such that you can use both log rule AND partial fraction decomposition to integrate it. Use these two methods to integrate the rational function.

Q: What kinds of functions can be integrated using partial fraction decomposition?

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Q: Use partial fraction decomposition to evaluate the integral. ∫6x2-13x+3/x2(x-3) dx

A: Refer to the question we need to find the integration using partial fraction for the provided…

Q: Use partial fractions to find the indefinite integral.

A:

Q: Use partial fractions to find the indefinite integral.

A: Given: I=∫x2+12x+12x3-4xdx For evaluating given integral, first we simplify given expression then…

Q: Using partial fraction decomposition, f dx is equal to: (x-2)(1-x)

A: We have to do partial fraction first.

Q: 3x4 – 8x3 + + 3x2 + 4x +1 x³ – 2x2 + x dx

A:

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: The technique used to prove that x4 - 2x + 2/2tan-1 3 X + C 2. dx = - - x² + 2 is Long (Euclidean)…

A:

Q: Without evaluating the constants, the partial fraction decomposition for 5x² – 3 f(x) (х3 — 4x)(x2 —…

A: Finding the partial fraction decomposition without evaluating the value of constants

Q: -5 1. S da (a+1)* (a-1)

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: 2. Give the form of the partial fraction decomposition of the rational function 3x2 + 2x – 3 f(x) =…

A: We have to give the form of the partial fraction decomposition of the given rational function.

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

A: Given∫x-9(x+5)(x-2)dx

Q: Use the method of partial fraction decomposition to perform the required integration X3 dx (x-7)2…

A: to given

Q: Solve the integral using partial fraction decomposition method, four digits after comma: 5x2 - 8x +…

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Q: Use partial fraction decomposition to integrate  ∫(x-9)/x^2(x^2+9) dx

A:

Q: х4+8х2 +8 dx e. х3-4х

A: Explanation is given below....and solve the integration

Q: Using decomposition into partial fractions, 4x2 + 2 J x(x² + 2) is equal to

A: We can solve this as follows:

Q: Fraction Decompositio

A: Given the  integral: ∫( (12x^4-6x) / (x^2-1) ) dx To solve by using  the method of Partial Fraction…

Q: Expand the rational function 16 / (x2+x+2)(x−1)2 into partial fractions.

A: We have to

Q: x° – x + 2x –2 dx 3 ?6 -2х + 2) X

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Q: Evaluate using Partial Fraction Decomposition: (- dx

A:

Q: A +B + C +スt X (x+D (x+1)" (x+2)

A: Using partial decomposition method

Q: Use partial fractions to find the indefinite integral…

A: Evaluate: ∫x2-6x+2x3+2x2+xdx

Q: dr š + 2r³ + x

A: Here I am attaching image so that you understand each and every step.

Q: Use partial fraction decomposition technique to evaluate the integral: S; dx. x² (x+1)³

A: ∫x21+x3dx

Q: The technique used to prove that x4 x3 - 5x + 5V5 tan¬1 3 x² + 5 dx + C - - is Long (Euclidean)…

A:

Q: Use partial fraction decomposition to integrate the given function  ∫x+6/x(x+2) dx

A:

Q: x³x² j - 7x + 13 x² - x - 6 -d.x

A: Given is ∫x3-x2-7x+13x2-x-6dx We need to evaluate the integral using partial fraction. Following…

Q: The form of the partial fraction decomposition of a rational function is given below. 16 – (x² +…

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Q: Use the partial fraction decomposition method to find the antiderivative of the function h(x)=…

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Q: arctan (Vx) dx

A:

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

A: Given

Q: ind partial fraction decomposition 6x+4/x^2+2x-15

A: Given: y=6x+4x2+2x-15 For finding partial fraction decomposition of given expression, first we…

Q: Integrate by partial fractions decomposition. 6-4x dx x' – 3x2 – 4x -

A:

Q: Find the partial fraction decomposition of the rational function.

A: It is observed that for the function 2(x-1)(x+1),the factors are x-1  and x+1.The partial fraction…

Q: 1 Integrate by partial fraction decomposition x² - 5x +6 .2 X

A:

Q: Integrate the rational function by partial fraction (decomposition): 2-9-dx r3-9x

A: Let I=∫x2-9x-9x3-9xdxApply the Sum Rule:…

Q: x² -1 dx x3+x

A: To find the integral

Q: Evaluate using Partial Fraction Decomposition: S x2 (x+1)²(x-1) -dx

A: We know, ∫dxx-a=lnx-a, for any real number a ∫dxxn=x1-n1-n, for any real number n.

Q: Without evaluating the constants, the partial fraction decomposition for 5x2 – 3 - f(x) : %3D (x³ –…

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Q: ∫ ((5x^3+2x^2+x-1)/(x^4+x^2) ) dx

A:

Q: Using partial fraction decomposition, dx is equal to: (3-x)3(2-x)

A:

Q: 2. Integrate the rational function below without using partial fraction decomposition. S -dv

A: Integrate the rational function below without using partial fraction decomposition v2/(v6-1)

Q: 5. Write out the form of the partial fraction decomposition of the integrand (Do non find the…

A:

Q: 4x By using the partial fraction decomposition - dx can be written as x2-2x-3 of(当,) 3/4 1/4 dx x+1…

A: We have to find

Q: Using decomposition into partial fractio 2x2 + 2 x(x2 + 2) is equal to

A: We have to find solutions

Q: Write out the form of the partial fraction decomposition. (Do not find the numerical values of the…

A: Both the questions are based on partial fraction.

Q: 4 Using partial fraction decomposition, J -1(2-x) -dx is equal to:

A: Using partial fraction decomposition,

Q: After finding the partial fraction decomposition, 7x2 + 5x + 13 -dx = (x² +4)(x – 1) dx Notice you…

A: Given:  Let I=∫7x2+5x+13x2+4x-1 dx  To Find: The partial fraction decomposition

Q: 5a2 +32-2 -dx (z-1) (2+z+1)

A: Let I=∫5x2+3x-2x-1x2+x-1dx First decomposing the given function using partial fraction…