Evaluate the Definite Integral using integration r19 by parts : In(3x) dx 1 o 19 In(57) – In(3) 18 - O 19 In(57) + ln(3) 18 - O 19 ln(57)+ In(3) o 19 In(57) – In(3) 20 - 20 -

Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 6tj – 6ik) dt

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Q: Evaluate the integral. (Use C for the constant of integration.) (x2.8 + x-1.2) dx

A: Power rule

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(In 12x) dx Cos In x +…

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Q: Evaluate the integral. (Use C for the constant of integration.) 9x3 + 2x2 + 27x + 2 dx (x2 + 1)(x2 +…

A: We have to evaluate the integral by using partial fraction

Q: Find the indefinite integral. (Use c for the constant of integration.) (4t°i + 12tj - 2VEk) dt

A: To find: ∫ 4t3i+12tj-2tkdt

Q: Evaluate the integral. (Use C for the constant of integration.) x2 dx 49 – x2

A: With the help of trigonometric substitution we can easily solve this question. Try putting x=7sin(t)…

Q: Find the general indefinite integral. (Use C for the constant of integration.)…

A: Find the general indefinite integral.

Q: Use the basic integration rules to find or evaluate the integral. e In(2x) 1+ ln 4 [eind X X dx

A: The given integral ∫1eln2xxdx

Q: (2+2æ) · e2z+z² dx as (2a + a2) · e2z+z² +C (2x + a²) · e2z+z +C

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Q: Find the indefinite integral. (Use C for the constant of integration.) | XV25 – (In x)² xp

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Q: Integrate the following indefinite integral to find the general solution using either the "evidence…

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Q: Evaluate the following indefinite integral. Use C for any constant of integration. * 4x³ + 8x² + 75x…

A: A detailed solution is given below

Q: Find the indefinite integral. (Use C for the constant of integration.) 2t dt 1- 4t"

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Q: Evaluate the integral. (Use C for the constant of integration.) (x^2-25)^1/2/x^3 dx

A: To find:-  ∫ √(x2-25)/x3 dx

Q: Evaluate the integral. (Use C for the constant of integration.) dx /x² + + 81

A: In this question given that a integration and solve it.  We use here integration formula and solve…

Q: Find the indefinite integral. (Use C for the constant of integration.) xp J xV81 - (In x)²

A: The given integral is ∫9x81-(ln x)2dx. The integration of 1a2-x2=sin-1xa+c, where c is constant.

Q: Evaluate the integral by making the given substitution. (Remember to use absolute values where…

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Q: Evaluate the integral. (Use C for the constant of integration.) dx x² + 81

A: Use substitution method to integrate. or   use ∫secθ dθ = logsecθ + tanθ + C1…

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

A: We can solve this by using substitution.

Q: Find the indefinite integral. (Use C for the constant of integration.) 5t dt 1 – 25t4

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Q: Evaluate the integral. (Use C for the constant of integration.) x² - 64 dx - +8

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Q: Find the general indefinite integral. (Use C for the constant of integration.) 4u5 - u3 du

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Q: Evaluate the integral. (Use C for the constant of integration.) x² - 16 dx +8

A: We have to find the integral

Q: Find the general indefinite integral. (Use C for the constant of integration.) (Sx² + 8 +) dx 4 x2 +…

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Q: Find the indefinite integral. (Use C for the constant of integration.) 7t + 4 dt

A: ∫e7t+4 dt = e7t+47+Cexplanation is given in below step

Q: Evaluate the integral. (Use C for the constant of integration. 9r15-r8 e

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Q: Find the general indefinite integral. (Use C for the constant of integration.) - 3u4 ته( ل u? +)

A: This question can be solved by using some basic formulas of integration like ∫xndx

Q: Find the indefinite integral. (Use C for the constant of integration.) 8. xV 64 – (In x)2

A: Consider the integral: ∫8x64-lnx2dx…

Q: Find the general indefinite integral. (Use C for the constant of integration.) (x1.3 + 11x4.5) dx

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Q: zv Evaluate the following indefinite integral using Substitution: V4.x2 + 4 dx

A: Given query is to eveluate the integral.

Q: Evaluate the integral. (Use C for the constant of integration.) x² + 7x + 1 (x² + 1)2 xp

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Q: -1 Cos'x 4. | X. dx 1-x* 2 dx 3 (x² + 2 + 2x + 2)2 5.

A: 4). Given: I=∫cos-1x1-x2dx    ...1   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: 33 = 1-

A: Here we evaluate the integral by using substitution method    ∫ dt/(1-3t)7 , u = 1 -3t

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) z2 dz 8 + z3

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Q: Evaluate the following indefinite integral. Use C for any constant of integration. 4x³ + 8x² + 75x +…

A: ∫f'(x)f(x) dx = ln f(x) +C ∫xn dx =xn+1n+1+C ∫1xdx =lnx+C ∫1x2+a2 dx = 1atan-1xa+C

Q: Find the general indefinite integral. (Use C for the constant of integration.) 3 4x2 + 5 + dx 2 X +…

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Q: Evaluate the integral. (Use C for the constant of integration.) (2× – 5*) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) (3* – 5*) dx

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(2x) 45 + cos (x) xp…

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Q: Evaluate the definite integral (exact value). 6. 132860 x5 In(x) dx =| 177147 In (3) – 9. For…

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Q: Evaluate the integral. (Use C for the constant of integration.) (3× – 5*) dx

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Q: Find the indefinite integral. (Use c for the constant of integration.) 4t°i + 14tj- 4vtk) dt

A: Given- ∫4t3i+14tj-4tkdt To find the given indefinite integral. Here we will use the following…

Q: Find the indefinite integral. (Use C for the constant of integration. 9. de cos(8) – 1

A: The given integral is ∫9cos(θ)-1 The trigonometric identity is cos θ=1-2sin2θ2 Integration of…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 8t dt 8t + 9

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 8t dt 8t + 5

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Q: Evaluate (x + 3) V16 - x2 dx by writing it as a sum of two integrals and interpreting one of those…

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Q: Evaluate the integral by naking the given substitution. Use C for the constant of integration) a* dx…

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Q: Evaluate the integral -3 dæ x² + 16 Note: Use an upper-case "C" for the constant of integration.

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Q: Find the indefinite integral. (Use C for the constant of integration.) 3t V9t4

A: Here, we use the formula shown on  board.

Q: Evaluate the integral. (Use C for the constant of integration) (X^7)/(e^3-5x^8) dx

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