20. +5, In Exercises 21 through 30, evaluate the indicated definite integral. 21. (5x4 8x +1) dx 22. (vi+r dt 23. (e2x + 4Vx) dx ² + Vx – 5 - dx | 24. 1 25. 30(5x – 2)2 dx (3x + 6) dx -1(x² +4x + 5)² 26. 27. 2te' dt x+ 1)2 dx X- 28. 29. dx

Q: Evaluate using integration by parts. .6 In (x)dx 6 In (x)dx =| 1 (Type an exact answer.)

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Q: Evaluate the integral dx 2x x - 3x? 1 V3 + V2 x u- - V7 VX + C 2/3 TV3 1 In 2/3"/7x + V3 +C -In 4…

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Q: 4) Solve the integral: Show work 10x2-48x + 160 dx (x - 4)2 (x2 + 16)

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Q: •12 Evaluate the integral dx dy by reversing the 3 order of integration.

A: To evaluate: The integral of ∫012∫y34ex2dxdy by reversing the order. Explanation: Consider the image…

Q: We have determined that du = 5x* dx. However, the given indefinite integral dx does not conta %3D x…

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Q: 3. (5 marks) Evaluate the integral I = dx. Hint: If you need to evaluate fe da, don't! Try a…

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

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Q: (2x+5)² 19. What should be the rewrite of the integrand of S -dx so that the resulting integral is…

A: Given query is to rewrite the integrand in integrable manner.

Q: In Exercises 1–8, decide whether the integral is improper. Explain your reasoning. dx dx 1. 5х — 3 -…

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Q: Evaluate the integral: Se3+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 - + C (3e)3 + cosh2x B…

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Q: 3 Calculate the integral: dx x² V25 + x2

A: Here first put x=1/t and then the expression inside the square root as y^2. As showing in solution

Q: 2.) Evalvate the Integral ودل أاد-ل (x² _33² dx, .3 2 by making w - x²-3 NOTE: Answer should be in…

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Q: dr

A: Given integration is : ∫x2-9x3dx To find the value of integration.

Q: (a) Define a substitution variable u and write / x(x +1)*dx in terms of u. Do not solve the…

A: detailed solution is given below

Q: 13. Consider the integral | - dx then (which statement(s) is/are correct): x2 - 4x (i) dx : x - 4x…

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Q: 8. The integral What is the value of A. B. can be rewritten as 15x²x³43x - 19 (x + 1)²(x² - 6x +13)…

A: Let's find.

Q: 3. Evaluate the indefinite integral 1 -dx x' + 3x? 3

A: Given,

Q: 2 1. Find the indefinite integral. Sáre 4x2 | 6xe dx 3 4x a. 2 3 4x2 +C c. 4&r°e*x*+C 2 4x2 +C +C b.…

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Q: / 2) + (2 / √x)) dx 2. ∫ ((t√t + √t) / t2) dt

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Q: x³ + 6x2 + x+2 2 Tan Ve fx-1 ax + In{(x+ 1)*(x² – x + 1)"| + The resulting integral of -X+ -1 + C,…

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Q: 33. Use integration by parts to find the indefinite integral. fxcos(2x)dx -xcos(2x)–sin(2x)+c а. b.…

A: To find the integration

Q: Which of the following integration expression can be transformed into integral of power 2 dx (A)…

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Q: Step by step

A: Given integral

Q: Find the indefinite integral using the Chain Rule/U-substitution. 6x dx x2+5 3. 4. S 7xv3x² + 8 dx

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Q: Step by step

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Q: 6) Evaluate the improper integrals ∞ 5 a) 5² (+ + e-") dx s (-x) е 2 7 5 b) ² = 8 dx 4x-8 2

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Q: State ALL the theorems on integration used in the following computation: 2 2 (32- 3 d - 23 3 3 -0) –…

A: Remark: The sum rule of integration is  ∫ ( f ( x ) + g ( x ) ) d x = ∫ f ( x ) d x + ∫ g ( x ) d x.…

Q: 3 9-x 9-x2 Evaluate the integral dz dy dx. 0 0 . 0

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Q: 2- What is the solution for this integral? x²e¯* dx a) e-*(x² – 2x + 2) + C b) -e-*(-x² + 2x + 2) +…

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Q: Which of the following integration expression can be transformed into integral of power (Ju"du). (c…

A: A

Q: Step by step

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Q: (2x+5)² 2. What should be the rewrite of the integrand of ſ x2 dx so that the resulting integral is…

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Q: 4. Evaluate the improper integral. dx х2 — 1

A: Consider the given integral as Solving the integral

Q: 3. If f f(x) dx = 13 and , g(x) dx = 4, find [ [3f(x)+ 4g(x)] dx **SHOW EVERY STEP USING THE…

A: If ∫07f(x)dx=13 and ∫07g(x)dx=4Find ∫073f(x)+4g(x)dx

Q: 4. Determine the following indefinite integrals: a) S(2x + 3x -7x2 + x-5) dx %3| b) S(x – 5)² dx g)…

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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: 02:- By using integration by part, find :- (Choose two only) 1- Sxe-* dx 3-S(1+ x²)e¬*dx 2-f Inx…

A: As per the company guideline's we are supposed to answer first question as mentioned by the…

Q: 3-Evaluate the integrals in Exercises: 2√3 So dx √4 + 4 + x² 0 4- 6 dx 5. Sot v Jo V1 + 9x² cos x dx…

A: We have to evaluate the integrals.

Q: Evaluate the integral. 고-36 x² – 36 . 6cos- (승) +0 /x² – 36 - dx = Vx² – 36 – 6cos¬! + C x² – 36…

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Q: ITT 6 136,- x 36- x2 dz dy dx. Evaluate the integral, 36,-x2 36- x2 dz dy dx=O 0 0 (Type a…

A: Given integral   I=∫06∫036-x2∫036-x2dzdydx

Q: Find the general indefinite integral: 1) S(x13 + 7x².5)dx 2) S Vx5 dx 3) Sv(v² + 2)²dv 4) Sx³cos(x*…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

Q: -1 sinx dx %3D

A: ∫01/2arcsin(x) dxIntgerate by parts ∫fg=fg=∫f'gf=arcsin(x),…

Q: Evaluate the integral. 6x2 sin AX dx Step 1 To use the integration-by-parts formula u dy = uvV – v…

A: Given:

Q: Evaluate the integral: sinh 3x csch 3x dx coth 3x "+C 3 coth X +C 3 - coth x +C - 3 - coth 3x +C 3

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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: Compute the definite integral 2 dx Vx² + 4

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Q: ∫(−2x2+6x−6)dx   Select the correct answer below:   a. 2∫x2dx+6∫xdx+6∫dx   b. −2∫x2dx+6∫xdx+6∫dx…

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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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