Express the integrand as a sum of partial fractions and evaluate the integrals ∫ 1/ x^3/2-√x dx     1 is the numerator while x^3/2-square root of x is the denominator

Q: integral

A: We have to calculate the given indefinite integral according to the given information

Q: Express the integrand as a sum of partial fractions and evaluate the integral. 25dx (x² - 1) ²

A: Solve the problem as shown below by using partial decomposition fraction.

Q: express the integrand as a sum of partial fractionsand evaluate the integrals. ∫ x2/x4 - 1 dx

A: ∫x2x4−1dxFirst we factorx4−1=(x2)2−(1)2                                        =(x2−1)(x2+1)…

Q: Express the integrand as a sum of partial fractions and evaluate the integral. + 5x + 10 xp- x3 - 1

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Q: express the integrand as a sum of partial fractionsand evaluate the integrals. ∫ dx/x2 + 2x

A: We write the integrand using partial decomposition

Q: Please check the convergence of the integral. 2 1 dx 2x- x²

A: To check the convergence of the integral.

Q: dx (x² - 1)²

A:

Q: Express the integrand as a sum of partial fractions and evaluate the integral. dx 4 - 9x2 ... dx %3D…

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Q: express the integrand as a sum of partial fractionsand evaluate the integrals. ∫ dx/(x2 - 1)2

A: Using partial sum we get:

Q: Express the integrand as a sum of partial fractions and evaluate the integral. 22dx S 2 x²-1

A: This question is based on indefinite integral using partial fraction.

Q: Use partial fractions to find the indefinite integral ∫ x / (16x4 − 1)    dx

A: We need to solve the integral using partial fractions.

Q: express the integrand as a sum of partial fractionsand evaluate the integrals. ∫ 8x2 + 8x + 2/(4x2 +…

A: Explanation: Given that,                            Now use the partial fraction  Now find the…

Q: Find the lower bound of sum 2-1 using an integral

A:

Q: 3x + 5 dx, ] (x + 1)(x – 3)²

A: ∫3x+5x+1x-32dx

Q: Use partial fractions to evaluate the integral 81/(( x^2)(x−9)) dx.

A: Explained below

Q: Express the integrand as a sum of partial fractions and evaluate the integral. 25dx (x² - 1)2

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Q: Evaluate the integral by integration by partial fractions

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Q: x*+2х+3

A: We can find the integration as below.

Q: express the integrand as a sum of partial fractionsand evaluate the integrals. ∫ 1/x4 + x dx

A: Given         ∫1x4+xdx

Q: •4 x dx 10 x2 – 9

A:

Q: Evaluate the integrals that converge 32 1 dx 2 ㅇ x5

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Explain the steps for evaluating integrals by using the Partial Fraction and give one  example each…

A: We know that a rational function is represented as a ratio of two polynomials, where g(x) ≠ 0. Two…

Q: Evaluate the integral using partial fractions: ∫ x+4 / x2+2x+5 dx

A: Here we use partial fraction and integration of the particular function : ∫dxx2+a2=1atan-1xa+C

Q: express the integrand as a sum of partial fractionsand evaluate the integrals. ∫ x2 + x/x4 - 3x2 - 4…

A:

Q: Express the integrand as a sum of partial fractions and evaluate the integrals. x+9 S: -dx 3 2x - 8x

A: see below the answer and calculation

Q: Express the integrand as a sum of partial fractions and evaluate the integrals. x+7 xp- 2x° - 8x

A:

Q: dx 21 VI(Vx + 1)'

A:

Q: Express the integrand as a sum of partial fractions and evaluate the integrals. x+9 S: -dx 2x³ - 8x

A: To express the integrand as a sum of partial fractions and to evaluate the integrals.∫x+92x3-8x dx

Q: Compute. integral x2arctanx dx.

A: It's a integral question so I'm provided hand written solution.

Q: Determine whether the improper integral converges or diverges. 7x +5 dx 2 1 Diverges O Converges

A: Here, to find the integral ∫1∞7x+5x2dx And, ∫1∞7x+5x2dx=∑n=1∞7n+5n2

Q: 9 dx. +x – 20 х2

A:

Q: Use partial fractions to integrate: 1 dx 5x? + 6х +1

A: Consider the provided integral, ∫15x2+6x+1dx Solve the provided integral by using partial fraction.…

Q: Evaluate the integral by Partial Fractions 6x? – 3x dx. (x – 2) (x + 4)

A: To integrate ∫6x2-3x(x-2)(x+4)dx, take the partial fraction of ∫6x2-3x(x-2)(x+4)dx and obtain…

Q: Express the integrand as a sum of partial fractions and evaluate the integral. 3x2 - 11x + 4 dx x3 -…

A:

Q: express the integrand as a sum of partial fractionsand evaluate the integrals. ∫ x + 4/x2 + 5x - 6…

A: the given integral is: ∫x+4x2+5x-6dx we have to express the integrand as a sum of partial fractions…

Q: Express the definite integral using summation notation: 4 (3*) dx 1

A: We will convert the given integral into summation notation using Riemann sum ∫14(3x)dx.

Q: dt 1³ +1²-2t

A:

Q: express the integrand as a sum of partial fractionsand evaluate the integrals. ∫ x + 3/2x3 - 8x dx

A:

Q: express the integrand as a sum of partial fractionsand evaluate the integrals. ∫ dx/1 - x2

A: To evaluate: ∫11-x2dx Given integrand can be written as: 11-x2=11+x1-x Using partial fraction…

Q: Express the integrand as a sum of partial fractions and evaluate the integrals. X +4 dx X +7x-8

A:

Q: Evaluate the integral by first performing long division on the integrand and then writing the proper…

A: Given problem:- Evaluate the integral by first performing long division on the integrand and then…

Q: Express the integrand as a sum of partial fractions and evaluate the integral. 4x3 - 5x2 + 8x - 10…

A: Given ∫4x3-5x2+8x-10(x2+2)(x-2)3dx Sum of partial fraction for the above question are Now consider…

Q: Express the integrand as a sum of partial fractions and evaluate the integral. 12x + 64 dx x3 + 8x2…

A: Given,          ∫12x+64x3+8x2+16xdx

Q: Express the integrand as a sum of partial fractions and evaluate the integral. 17dx 2

A: We have to express the integrand as a sum of partial fractions and evaluate the integral…

Q: Use the method of partial fractions to evaluate each of the following integral. Show your work!

A: To find the integration by using partial fractions

Q: 32. ³+x²+x+2 + 1)(x² + 2) dx

A:

Q: Express the integrand as asum of partial fractions and evaluate integral. 6x2 + x + 25 dx tx2 + 5)(x…

A:

Q: Use partial fractions to find the indefinite integral…

A: To evaluate the integral: ∫2x3-4x2-15x+5x2-2x-8dx Solution: We know that partial fraction can be…

Q: 4x2 – 1 -dx. J 3(3x + 1)

A:

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

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