Make a substitution to express the integrand as a rational fun- 4e2x e2X + 10ex + 21 dx

Q: accidently posted two questions. with this one

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Q: Evaluate using Integration by Parts, substitution, or both if necessary. (Use symbolic notation and…

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Q: Perform the integration: S 9x² In x dx A None of the choices are correct. B 3x In x- x/3+C 3x In…

A: We have to integrate.

Q: Evaluate the integral: e3x+4y dA, R = [0,9] × [0, 1] R Answer :

A: Evaluate the double integral

Q: INTEGRATION BY SUBSTITUTION Using dt 1. 1? - q² = 2a In + C t + a where a e R, find dx 4x2 – 11x + 2…

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Q: 2 12x³ –6 Evaluate the definite integral: ;dæ aª – 2x+7 1 Note: Express your answer in exact terms.

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Q: 2r2 + 2x + 11 dz J (2r + 3)(22 + 4)

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Q: Evaluate the integral. dx 3. xª/x² + 27

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Q: Q3. a) (i) Evaluate the following integral using integration by parts Se²x co e²x cos (2x + 2)dx…

A: Dsclaimer: Since you have asked multiple question, we will solve the first question for you. If you…

Q: a. Evaluate the integral ∫ (4x2 + 2x -1) / (x3 +x2)  dx b. Evaluate the integral ∫ x3  /…

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Q: 3z - 3r+2 dr. (x-1)(x2 +1) Evahuate the integral

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Q: the integral. (Use C for the co + 16x + 1 xp (x² + 1)2

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Q: 16 -3t – 3 What is the value of the definite integral dt? Enter your answer as an exact fraction if…

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Q: Solve the separable equation using the integral factor  y⁴ y¹ +y¹ + x² + 1 = 0

A: Given equation is y4y'+y'+x2+1=0solve it

Q: 3x²-4x+5 between 2 and 3. x³ x²+x-1 Find the integral of f(x) = 31

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Q: 13.Using integration by substitution in f'æ° (x® – 2)*dæ ,what is du? O A (26 – 2)³ dx (xº – 2)dr…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4. Evaluate the integral below by following a series of steps: 2x +3 J 4x² + 5x + 6 (a) Evaluate f…

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Q: 1 8х —1 х? +х- 6

A: Use the partial fraction to evaluate it. A detailed solution is given below.

Q: Make the u-substitution 2 sin x = 2u 1+u²⁹ COS X = 1-u² 1+ u² and dx = du 1+u² to convert the…

A: To evaluate the given integral.

Q: 8) A rational function has a HA at y = 2, an x -int of a VA at x = -4 and a y-int of - 3 Determine…

A: Given that the VA is x=-4, this means the denominator has a factor= (x+4) Given that the x-int is…

Q: 1. Kgothatso showed her classmates that dx%3D (x- 1) Without showing Kgothatso how you would…

A: 1.AgreeGiven Integral can be evaluated with the formula :∫yndy =yn+1n+1here y =x-1 , n=-23

Q: Hi could you help me solve the integral of e^(x/2) in contrast to the integral of e^(2x)? I…

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Q: where does the number that you subsitute in the subsitution method come from? In this case where did…

A: Given,

Q: Jse the symmetry of the function to simplify/evaluate the integral, 3. (2+ |x|5) dx. -3

A: Please refer to the image below.

Q: 4 When you evaluate the integral (8x- 12) (4x2 – 12x)" dx using u substitution, the integral you…

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Q: (x2 + xp: a²)²

A: Take the function out and evaluate the indefinite integral. ∫x2x2+a22 Here, x2+a2 can be written as,…

Q: Evaluate the integrals. ∫ (a2-y2)5 y dy

A: ∫a2-y25 y dy Put, a2-y2=t⇒0-2y=dtdy⇒-2y dy=dt⇒y dy=-dt2

Q: 9. To evaluate -5f(x) dx, use the following property of the definite integral. 9. kf(x) dx = f(x) dx…

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Q: -S 3x²-6x+7 x3-x²-x+1 dx

A: The given integral is ∫3x2-6x+7x3-x2-x+1dx. The objective is to evaluate the given integral using…

Q: Use substitution to convert the integrals to integrals of rational functions. Then use partial…

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Q: dx Using an appropriate substitution, the integral V-x-6x+40 is equal to: (Complete the square, if…

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Q: Find R3.3 approximation of the integral. c1 v3

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Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

A: The solution is given in the next step.

Q: f(x) = х — 2 36 35 x-1 what is the X - 1' smallest integral value of x that gives an integral value…

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Q: Integrate the Following using Rational Functions 2.х2 — 9х — 9 -dx x3 – 9x (a) / (b) /: - - 1 d.x…

A: (a) ∫2x2-9x-9x3-9xdx =∫2x2-9x-9xx-3x+3dx=∫2x+3+1x-1x-3dx=2∫1x+3dx+∫1xdx-∫1x-3dx=2·lnx+3+lnx-lnx-3+C…

Q: (a) (b) Evaluate S 9xsin (2-3x)XAMIMATION dx. *1*: FIDENTIA Evaluate 1 9x² +6x+ AL 123 CALCULU by…

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Q: Use substitution to find an indefinite integral with the power rule Question -4x2 (4x³ – 1)' dæ. Do…

A: Use the substitution method and find du.

Q: To convert th Integral dr tnto an integral of rational function of is to use the substttution x- a)…

A: Use √a=x  Becomes a=x2 And simply the question to get the correct answer.

Q: =iven √x³√4-x² dx. If we letz= √√4-x², which of the following integrals is correct using…

A: We have to substitute z=√(4-x^2)

Q: Q18: Evaluate the definite integral: 4x dx V1 + 2x²

A: To find the definite Integral  Substitute 1+2x^2 = t and change the limit accordingly

Q: Solve the separable equation using the integral factor  2xy + 6x + (x²-4)y¹ = 0

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Q: = -19 when x = Integrate the following expression, and solve for the constant of integration using…

A: It is differential  equation

Q: Evaluate S x(x + 2)2 dx by two methods: (a) Expand (x² + 2)? and multiply the result by x; (b) let u…

A: Given : integral of x(x² + 2)² dx

Q: dx S x2 ( 4. x²+x+1)

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Q: df Use integration to find f(4), if = dx O -26.667 O -19.667 O 26.667 O 30.333 5x2, and f(1) = 7.

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Q: x'dx The integral expression can be evaluated using integration by parts of the form udv = vdu Using…

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Q: Can you help with this problem step by step?

A: We take h=b-a/n, and as n approaches infinity , h approaches 0.So, given equation become