x² – 29x + 5 dx (x–4)'(x² +3)* + 3

Q: (2x + 4) + 1 dx- x² + 4x + 5 x² + 2x– 10 2 (2x + 4) + 1 2 Consider dx = x2 (x² + 4x + 5) dx.…

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Q: 9-x² - y² SS. 0 9-x² 0 √√x² + y² dz dy dx 2

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Q: x- /= ² + √²-11 de dx dx x-1 x² + x + 1 3

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Q: dx 3. 4

A: We have to find the value of the integration                            ∫xy2+x2432 dx Since we have…

Q: dx Integrate: S x²-3x+2

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Q: H-w 2x +3 dx メ+2 X X 3 X2+ 2X+1

A: Topic:- application of integration

Q: 3x +2 J. - dx. (x² +9)(x– 4)x 10. Find the principal value of

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Q: x2-4x dx 3) S (x+1)(x²+4)

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Q: 2dx J x (3(ln x)2 + 12 In x – 15)

A: The given integral can be evaluated using the factorization and substitution technique.

Q: 2-x 4x + 4x - -m(4x* + 4x – 3) + In| (2x 2x- – 3 x +1 x(x + 3)(x + 2)(x – 1) 1 (x + 3)*(x – 1)ª I…

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Q: (1) f(x+4)² dx (3) ſ. x² dx x² - 4 (2) √ x²(x³ + 1)² dx (4) √x²0 x² cos 3x dx

A: The given integrals are;  1) (x+4)2 2)x2(x3+7)7 3)x2/(x2-4). Repost the 4th question.

Q: 27. ·√ √(x + 2√1-x²) dx _28. [₂ (2+√9 − x²) dx -3

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Q: Sla 1 z dx |(25 – x²)3/2]

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Q: 1) Evalvate - 5 dx ZV5 arctan x - 5 5 2 /5 arctan X-5 +C 2 x* - 5 arctan 5 arctan 25

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Q: (iv) S х2 +3х-1 dx x3-1

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Q: コ-6 dx 1十XS

A: Given Data: Subdivisions: n=6 Integrand: ∫0311+x5dx Function: fx=11+x5 Lower limit: a=0 Upper limit:…

Q: Solve th D.E using Exact -(3x² – 6.xy)dx +(-3xr' – 2y)dy = 0

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Q: dx 1- S 4+x2

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Q: Find df^-1/dx for f(x)=x+3/2x+5 at x=3

A: The given function is: f(x)=x+32x+5 Let g(x)=f-1(x). So,…

Q: (a) S v16 – 9x²dx using th - (b) dx using thes V9-x2 dx using the subs

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Q: X 3- Ssin ² x dx ។

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Q: 1 7) So dx V36- x2

A: Solution of the problem as follows

Q: x2 - 3x/5 + 1 dx 1/2 3r7/s

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Q: 5. (x² + y²)dx – 2xy dy = 0 -

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Q: -1)/(x4))1/2

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Q: 5) (2xy -3y) dx + (x-x) dy = o

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Q: 2+ X 50 -x + 4y dy dx 2-X

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Q: :) 3 1 19. + dx x3 3x 20. | (2.x2 + x – 1)dx 2y4 + 1 / 2y4 Зуз 21. ip- 1 1 22. / (VE+1- + sin x – e"…

A: 19.  Let the given be I  I = ∫3x3 - 2x3 + 13xdx Now integrating given integral , we get  ⇒I = ∫3x-13…

Q: -16 dx 1. X=2 sec(e) 2. x= 2sin(e) 4-X dx 3. X= 4tan(e) 4. X= 4sec(e) SV16+ x² dx x²-4 dx

A: See the details solution in below

Q: dx S- x4 - 1

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Q: х — х* - 3х - 2 X | dx x* - x'+ 4x – 4x 3

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Q: 2 S. x*- 4x +4 dx (メ-2)(x4) |

A: Solution: Consider the given integral is: I = ∫x2-4x+4(x-2)(x2+4)dxI = ∫x-22(x-2)(x2+4)dxI =…

Q: x2 - 10x - 5 dx J (x - 1)2(x² + 1)

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Q: b. Find S 5x*(x5 – 1)dx using a suitable substitution.

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Q: -4 (1x|+x-2|) dx -1

A: To find: The integral ∫-14x-x-2dx. Concept used: The absolute function fx=x: fx=x,    x≥0-x, x<0…

Q: (4) (2xcosy+3x²y)dx+(x³ – x²siny-3)dy=0

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Q: x*dx 3. S x2-1

A: use a partial fraction to solve the integral.

Q: (4(x2-1) dx x²(x+2)

A: We will use partial fraction here

Q: [4] s **-2x³-2x x²+1 [4] S² > [5] S dx dx ex-1

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Q: ¹In(1+x) -dx X

A: According to guidelines we must answer only one of the multiple questions given. So, I answer only…

Q: | 3tan-1(x)dx = %3D 2프-21n2 In(4) 2/3 None 을 + m2 2 In(÷) | 3 3 - In(4) 6 3

A: Solve by parts method of integration.

Q: x² +x-2 -dx can be resolved into (x2-1)(2x-x²)

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Q: ∫[(1/ (x2√(4 - x2))) dx] Please show all work

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Q: (メ2メ+Sx )dx h- Cos3x dk 120 x3-XSinx+ CusX dx C. 130 x41 (2メーリdy

A: As per our policy, I can only provide you solution for first three parts, but part (c) is not clear…

Q: x +1 Evaluate the integral dx. Vx2 + 2x + 3

A: Note: for given integral none of the option is correct match.I have solved as per integration by…

Q: ' 7 cosh (x) dx = 1

A: We have to evaluate the integral ∫197coshxxdx

Q: .3 2х+x-1 4. J dx х3+x2—4х-4

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Q: 2 dx X + X - e メ-

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Q: 2x +1 S- dx x(x² +16)

A: Find the integral by partial fraction