Let a, b, and C be a constant, verify the following indefinite integral. IVa+bx dx 2 (3bx – 2a)(a + bæ)³/2 + C. - 156

Q: 53. Use the substitution u = x + 1 to evaluate the integral I dr.

A: Differentiate u with respect to x,  du= 4x3 dx du/4x3= dx

Q: Write the integral in terms of u and du. Then evaluate:  ∫ (x − 7)3 dx, u = x − 7

A: ∫x-73 dx Put, u=x-7⇒dudx=1-0⇒du=dx Therefore, ∫x-73 dx=∫u3 du

Q: Evaluate the given indefinite integral. Indicate u, n, and du. xdx хах 3-x

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Q: Use the substitution u =x +7 to evaluate the indefinite integral below. 5 + Write the integrand in…

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Q: 3x2 dr. In evaluating by substitution, if u =x+1 then what will be the resulting xP+1 indefinite…

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Q: Evaluate the integral х3 dx x2 +49 х3 dх x2 +49 (Use C as the arbitrary constant.)

A: We substitute x^2+49=t, then the given integral become

Q: (D) What is the value of the original integral in terms of x? -30V z2 + 25 X + C 25z

A: Using substitution we have

Q: (a) Evaluate the integral using the substitution u = In (5x). x In (5x) dx x In (5x) ? Edit +C (b)…

A: An integral in some cases can be simplified using a substitution. For example ∫ln(x)xdx with the…

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) 1 9…

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Q: -(-3у?-у-2)dy 2y3+y2+4y

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Q: Evaluate the integral. (Use C for the constant X - 7 dx x2 - 18x + 82

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Q: Evaluate the integral ? e1/x dx x2

A: we have to integrate by using substitute method

Q: D= XP, - (8 + 2x) xZ XP, - ( + 2*)x<] Evaluate the indefinite integral by using the substitution u…

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Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫(x + 1)12…

A: Given: ∫12x+1dx for evaluating this integral we substitute u=x+1 now differentiate both side with…

Q: x²e²³, dx

A: The given integral

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dx,…

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Q: 21. Write the definite integral that repre formed by y = x² + 2x + 1 and y=2x+5. Do:

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Q: Which one of the following integrals would result from making a u-substitution in order to find the…

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Q: Suppose we make the substitution u=2+x in the indefinite integral da. What is the resulting…

A: Given Data: Integrand: ∫x42+x5dx Substitution: u=2+x5 ......1 Use derivative to obtained another…

Q: (뚜 - 굶) da 3x Evaluate the integral J (* – 3) dx.

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Q: Use symmetry to evaluate the following integrals. 1. 10 A00- 2. (1-1피)dr

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Q: What u-substitution should be made in order to evaluate the following integral? dx (6x² + 4)* u =

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Q: y + 2 Vhat is the indefinite integral of dy ? (y² – 1)(y² + 1 )´)

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Q: dx x²/16-x 22.

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Q: Write the integral in terms of u and du. Then evaluate. | (3x – 1)° dx, u = 3x – 1 (Use symbolic…

A: Solved below

Q: Evaluate the following indefinite integral. Do not include +C in your answer. |(-2,8 – 2æ" + 2x –…

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Q: A. Evaluate the following integrals by substitution. 1. Sx(2x? + 3)®dx

A: Put (2x2+3)= t  Differentiating both sides  4x dx= dt

Q: Evaluate the given indefinite integral. Indicate u, n, and du. xdx 3-x

A:

Q: (a) Evaluate the following indefinite integrals: (i) 10 (ii) fx³ Vx-1 dx 2 -Vy - 3 Vy 4

A: Evaluate:

Q: しx(x*+) dx

A: Integration

Q: Evaluate the integral by interpreting it in terms o 0. 9 - x2 ) dx -3 9 3 + 4

A: ∫-30 (3+9-x2)dx=∫-30 3dx+∫-30 9-x2dx                                    =A+BA:∫-30 3dx=3x|-30…

Q: Write the integral in terms of u and du. Then evaluate. / 6xe* dx, u = -x? (Use symbolic notation…

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Q: x? dx (x² – 25)5/2

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Q: 3x2 dr In evaluating by substitution, if u =x+1 then what will be the resulting indefinite integral…

A:

Q: In evaluating x+2 dx by substitution, if 4 =x+2 then what will be the resulting indefinite integral…

A: We will evaluate this as shown below

Q: Write the integral in terms of u and du. Then evaluate. xV9x + 4 dx, u = 9x +4 (Use symbolic…

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Q: Evaluate the given indefinite integral. Indicate u, n, and du. [5lan2P etan 28 sec² 2 Bd ß

A: Let I=∫5tan2βetan2βsec22β dβ

Q: In evaluating /x V4- x dx by substitution, if 4 = 4 – x then what will be the resulting indefinite…

A: ∫x4-x3dxu=4-x→dudx=-1→du=-dx

Q: Evaluate the integral 50 3)dx - by making the substitution u = x 6 – 3. + C NOTE: Your answer should…

A: We will integrate the following.

Q: For which constant B values is the integral o (3x2 + 2x – 3y, Bxy+ 4y) F. dr, F(x, y) ||…

A: Given,             F(x,y) = &lt; 3x2+2x-3y2 , βxy+4y&gt;To find →  (i) β such that ∫CF . dx is path…

Q: Write the integral in terms of u and du. Then evaluate. | (4x – 3)" dx, u = 4x – 3 (Use symbolic…

A: Integration

Q: Sx²e=* dx Sx²e¬

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Q: Evaluate the given definite integral using appropriate substitution:8 8e2 dr -4e4 + 4 ... 4e4 – 4…

A: We have to solve the problem

Q: Evaluate the integral

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Q: dx. ot Find the indefinite integral x4 = xp

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Q: In evaluating x+2 dx by substitution, if u =x+2 then what will be the resulting indefinite integral…

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Q: Evaluate the indefinite integral. fo(z - 7°dz + C

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Q: Evaluate the indefinite integral by using the given substitution to reduce the integral to standard…

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Q: 14. VE (t² + 3t + 2) dt

A: We use the formula integration of xn dx=xn+1/(n+1). See 2nd step.

Q: Evaluate the integral. x² + 49 dx

A: