Which of these is a non-elementary integral?" ( In(2y² + 1) -dy 4y A. * cosh(2x) xp. B. + cos(e-")]dx (x² + 2x + 3) D. x* – 2x + 1 dx

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Q: Find the general indefinite integrals of: 2. S Vx2 + 2x dx

A: First add 1 and subtract 1 so that make it x+1. Whole squre then put x+1=t. Then use the formula and…

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Q: 9. Find the integral, using u substituti x-(1-3x²)*dx a.

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

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A: The integration by parts formula is ∫udv=uv-∫vdu

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Q: 5. Compute the indefinite integral - 4e2* + 6x – 5) dx.

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Q: -1 tan 2y dy

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Q: 7. Which of these is a non-elementary integral? In(2y² + 1) А. -dy 4y e-x cosh(2x) В. c. [ e-x +…

A: Non-elementary integral for a given elementary function is an  indefinite integral that is, itself,…

Q: 2. Compute the integral dy dx by interchanging the order of integration.

A: Order of change of integrals

Q: S(1+- x3 dx 1+x2, 3

A: Topic- integration

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Q: Compute integral below with the use of substitution. eð 1 -dx x In° x

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Q: Approximate the integral from 1 to -3 of e-x dx using four equal subintervals.

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Q: Show using residues that   the integral from 0 to infinity of dx/(1+x^6) equals (2pi)/3

A: We have to show that ∫0∞dx1+x6=2π3 by using residue theorem. Now, ∫Cdz1+z6=∫−RRdx1+x6+∫γdz1+z6 Now,…

Q: (d) Prove that 1-cos 2x dx is divergent. Hint: Split the expression inside the integral into two…

A: Integral is converges or divergence

Q: What is the indefinite integral of (2/(x(x-2)^2))dx?

A: Use partial decomposition method.

Q: Evaluate the integral 4х + 5 dx. 3 - x2

A: To find the integral

Q: Evaluate the integrals in ∫e-1/x2/x3 dx

A: ∫e-1x2x3 dx Put, -1x2=t⇒2x3=dtdx⇒1x3 dx=dt2

Q: 2. Evaluate the indefinite integrals: D = tan r secʻ r dr 8x + 7 dr 72 +1 E = - 2dr F = dr V9 - 36x2

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Q: Evaluate the integral. 3y- cos xy dy dx x/3 O 5(1 - cos 3) O 3(1 - cos 3) O cos 3 -1 (1 cos 3)

A: Given: ∫03∫x313y2 cos xy dy dx We have x3≤y≤1 and 0≤x≤3 This can be seen as: We can change the…

Q: Identify which among the numbers are odd-numbered integrals. 1. S21 cos 7x dx 2. S csc* dx 14. S dy…

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Q: 1 The improper integral -dx is given by: x² +8x+41 Select one: O a. None of these sec-'((b+4)/5) de…

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Q: Evaluate the integrals

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Q: Compute the indefinite integral 2. 4e2a + 6x 5) dx. - -

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Q: Which of the following is NOT an improper integral? 0 2x of ₁7² +²22-3²² dx + 2x - 3 2x x2 2 - 3x e…

A: which of the following is not an improper integral??

Q: Compute the approximation  of the integral -4 to 4 e^(-x^2) using the trapezoid rule with n=4; you…

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Q: S dy V1+9y2 3.

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Q: Evaluate the integral. (In(x))² x3 dx

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Q: Which one of the following is a PROPER INTEGRAL? OA. .5 2x dx. 3 7x2-3x O B. dx. x In Oc. | x2…

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Q: Suppose we perform the substitution u=1+Vx in the integral dx . (1+Vx)5 What is the resulting…

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Q: 4. Prove using the results concerning iterated integrals that In 5 dx = 4 sin? x

A: Given:-                 To prove the result concerning iterated integrals that…

Q: - Prove using integrals Proper tos : e even sin()fc) dx=0 -b 9- For even functions.

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Q: Evaluate the Cauchy principal value of the given improper integral. 1 [ (x² + 4)² dx

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Q: 5. Find the particular integral of d²y + dy - x2 + 2x + 4 dx2 dx

A: We use the operator method to find the particular integral of the given differential equation.

Q: d) Prove the results of the integrals 3 dx = 2+ In (2)– 4 [In (5)– In (3)]. x² +3x +2

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Q: 2. Evaluate the improper integral S₂ (5. dx (5-x)4/3 or state that it diverges.

A: The given integral,      ∫28dx5-x43

Q: dx x (In x)5

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Q: 5. fx³√√4 - 2x² dx

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Q: Which of the following integrals are improper? (Select 3 L₁x²-1 dx 3x - 1 1 06²/21 x ² = 1 dx 2x 00…

A: Topic:-  improper integration

Q: 1. What should be A for the path independent of (2,4) xy + A dx + 2Ay – x y? fip- (1,2) Moreover…

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Q: 2 Evaluate the improper integral e4z dx, if exists. a) The nature of the integral is:

A: Explanation of the solution is given below...

Q: Evaluate Poisson Integral: In(1-2a cos(x) + a²) dx ,a.) [a| 1,

A: To evaluate Poisson's integral: ∫0πln1-2αcos(x)+α2dx  a)α<1 b)α>1

Q: find | (In(x)dx 2 3 Improper Integral

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