Find or evaluate the integral by completing the square. (Use C for the constant of integration.) dx x4 + 2x2 + 2

Q: Evaluate the integral | a (2° – 5)26 dx, by making the substitution u = x6 - 5. +C Note: Your answer…

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Q: 2) Find each integral by substitution a) [5x*(x' +7)'dx b) [x'e' dx

A: a) ∫5x4x5+73dx......(1) Put x5+7=t Differentiate the above function ddxx5+7=dxt5x4dx=dt Substitute…

Q: Using the method of substitution, b. x² V8x + 5 dx = f(u) du a vhere du dx = а — b = and f(u) = The…

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Q: Evaluate the integral. dx a > 0 + x²)3/2? 4 Jo (a2

A: given, 4∫0adxa2+x23/2 , a>0

Q: Evaluate the integral: 36 x dx + C

A: According to question given that ∫x336-x2 dx

Q: Evaluate the definite integrals -3 a) dx b) 1. 2 c) dx d) x² dx da

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Q: Evaluate the following integrals. 1 dx x²Vx2 – 9 3

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Q: 4. (ази t эзо

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Q: Given ∫(2x5+x3+6x−2)dx, evaluate the indefinite integral. Do not include +C in your answer.

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Q: Use integration by substitution to solve the integral below. Use C for the constant of integration.…

A: Given query is to find the solution of the integral.

Q: x/1 - x² dA; R = {(x, y) : 0 < x < 1, 2 < y < 3}

A: The double integral ∬Rfx, ydA is can be written as ∬Rfx, ydxdy. We have given the region R=x, y :…

Q: x² + 2 xp (х — 2)(x2 — 2х + 2)

A: The given integral is: I=∫x2+2x-2x2-2x+2dx   We know that; ∫1ax+bdx=1alnax+b+C

Q: Tπ L2 sin3xdx Tπ 4

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Q: dx h) S x2+4x+8

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Q: 1 el/x dx x3

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Q: Find the integral. dx x2 + 3 + C

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Q: Define a substitution variable u and write ;dr in terms of only u. (2x – 1)2 You do not need to…

A: Given: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 2T CSC X cot x dx

A: We have to solve the integral: ∫π32π3cosecx cotx dx We know the formula, ∫cosecx cotx dx=-cosecx+C…

Q: x² 2 :(a² + x²)ž + C 3 15 1 |x*(a² + x?)¿ dx = -

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Q: dx What is the result of integral ? le xln³x A) B) o C) D) – o

A: Use the substitution for Lnx=v

Q: Find the value of the integral T x² da (x²+9) (x²+4)²

A: To find- Find the value of the integral ∫-∞∞x2x2 + 9x2 + 42 dx

Q: Evaluate the integral. 5 22 e dx = +C

A: Note the following results in integration and differentiation :  ∫ab=a∫b-∫a'∫b    ..................…

Q: I² +x – 5 dr. I+3

A: ** As per our guidelines we are supposed to answer only one question at a time. Since you have…

Q: Find the value of the integral of , 2x? dx. a. 2 b.24 c. 6 d. 8

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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: a) S In Gxt1) dx 2.

A: In this question we have to find the Integration. Formula Used, - Chain Rule. - ∫lnx=1x+C

Q: Evaluate the following integrals. dr x²Vx² – 9 13

A: We put x= 3sec(u) and differentiate both sides with respect to u and find the value of the given…

Q: xV|x² – 9| + 7 dx

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Q: Find or evaluate the integral by completing the square. (Round your answer to three decimal places.)…

A: We have to evaluate the integral by completing square.…

Q: Evaluate the integral: S (3x-3 + 3)dx Choose the most appropriate answer.

A: ∫ 3x-13+3dx=∫ 3x-13dx+∫ 3dx=92x23+3xAdd a constant to the solution=92x23+3x+C

Q: dx 2x² 2. + 6

A: Given ∫4x2x2+6dx In order to solve the given integration first substitute 2x2+6=u and then proceed.…

Q: Use the appropriate technique of integration to solve the following. (a) In x? + 1dx

A: SOLUTION-

Q: Evaluate the integral. 17 x2 e" dx + C NOTE: Enter the exact answer.

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Q: Evaluate the definite integrals a) (бх? — - 2x – 10) dx = / (x+ 4)² dx = b) 1 c) (x* – x³ ) dx - ||

A: Some of the properties of integration  ∫abf(x)dx=F(b)-F(a) ∫xndx=xn+1n+1+C…

Q: Evaluate the integral. You may need to use substitution, complete the square, or some other method…

A: First make a complete square by adding and substracting 9 in  x 2+6x so that we get x 2+6x+9- 9…

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: Evaluate the integral: 6/ x² dx + C

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Q: Evaluate the integral and choose the correct answer. fxe² dx O Ọ xe ttc o xe etc Ọ - xẻ +C xe - 2e +…

A: Topic = Integration

Q: solve the given integration by substitution by sub

A: Given: ∫cos(lnx) dx

Q: Evaluate the integral. 16 x e3* dx = +C NOTE: Enter the exact answer.

A: We have to find the integral

Q: Find the integral ∫3e^3? d?

A: Given,

Q: 3. Which integral should be evaluated using substitution? 9dx (b) dx 1+x2 1+9x2 (a)

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Q: 2x2 + 2x + 11 dx (2x + 3)(x² + 4) (c)

A: Evaluating the integral using partial fractions.

Q: Evaluate the integral + 3)(x² + 3x + 5)* dx by making the substitution u = x² + 3x + 5. + C NOTE:…

A: We can evaluate the given integral by using the substitution u=x2+3x+5 and applying the following…

Q: Evaluate the integral. 5 x2 e dx +C

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Q: х+1 dx 3 2 2 25 - x

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Q: √ √ 1 √x² - 2x + 5 dx

A: Indefinite Integration

Q: Perform the integration. sinh? (e-) dx e cosh(e-) 2

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Q: By completing the square, dx the integral S is equal to: (x+5)Vx²+10x+21

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Q: x" In x dx

A: Given: I=∫xnln(x)dx