2x + x2 cos(x) + 1 -dx x2

Q: 2sinx (x)cos² (x)dx =

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Q: 5) y"-y'-2y=x+cosx

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Q: (b) (cos(x) (2x + 3))'

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Q: y = ce2x cos 3x + c2e2x sin 3x

A: By Bartleby policy I have to solve only first one as these are all unrelated & lengthy…

Q: Evaluate the integrals

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Q: 3π/2 3) 14 cos 2x dx п/2

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Q: 6. (a) cos 2x dx; u = 2x

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Q: x – sin 2x -dx x + cos2x

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Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: COs 2.r dx x² + 2x + 2

A: In this question, we find the principal value of the integral by using residue theorem

Q: Scos2x (2 2 Cos 2X (2 cos 2X -1) dx

A: Given integral is ∫cos 2x2 cos22x-1dx To find: Value of the given integral. Formula used: 1) cos…

Q: fe²x+Inx² sin x² dx = - +1/√√e²x cos x² dx

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Q: = Vx* – - 4 cos x+/7x %3D

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Q: f(x csc² 2x - x cos 2x)dx

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Q: Find integral.

A: We can integrate this expression by using integration by parts technique . From integration by parts…

Q: /2 2 cos x dx 1+ (sin x)² -n/2

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Q: (6e + 6x°+ 4 cos a + 2)dx 6e + x° + c 4 cos a + 2x +

A: Since this is a multiple question, according to the Bartleby answering rule, only first question is…

Q: (a) [- 9x2 +x° cos x dx = 3

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: cos2x a) -.dx,b) xe*. dy Į sin2x. [In(sin2x)]² + sin2x 0.

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Q: 2n 3. o (x + cos x) dx

A: Given :

Q: 1- x Vx2 + 9 dx. 1 2-5 dx 1+ sinx 3- sin'x cos'x dx

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Q: Evaluate D³(sinx - 4e²x) A -sin x-32e²x B -cos x-32e²x (C) с cos x-32e²x D sin x-32e²x

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Q: f(x csc² 6x - x cos 6x)dx

A: Given: I=∫xcsc26x-xcos6xdx   As we know that; The Sum Rule: ∫fx±gxdx=∫fxdx±∫gxdx And a).…

Q: -2/√√/3 dx x√√x²-1 • [²/²2 (x + 12/²3). dx sin² π/6 28. • √2 30.

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Q: integral cos^7(4x)

A: To find the integral

Q: 2x 2)/3x* 2) [3x* - 9x² +1 V9-x² dx .2 3) [ sin xcosx dx x cos.x 4) S sin² xcos 4) sin x cos x dx

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Q: 8. / (V80 – x² 0.3 cos(1.2x + 1.3) + 5) dx -

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Q: 3. fe2x+Inx² sin x² dx = = 2x -+√e²x cos x² dx

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Q: 5. (4xy-y²+10x²+sin x)dx+(2x²-2xy+ cos y )dy=0

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Q: -r°(1-cos2x) 1- dx 2

A: 1). To evaluate the integral: ∫π01-cos2x2dx Solution: Evaluating the given integral.…

Q: x2 Q1 (x sin x+cos x) -dx

A: For integrating the given integral we will use the below-mentioned integration formulas…

Q: x5-3 14. S4 cos (-3x + 2) dx

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Q: x cos x² 2. X C0 dx -siny

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Q: 1. (6x + f²)dx + f(2x – 3f)df = 0 2. (cos2f – 3x²f?)dx = (-cos2f + 2x sin2f + 2x³f)df 3. (fe*f –…

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Q: x° cos (3x) dx X COS

A: Integral by parts:∫ uv dx =u∫ vdx -∫(dudx∫vdx) dxI=∫ x6 cos(3x) dxu=x6, dudx=6x5v=cos(3x), ∫ vdx…

Q: [2xy cos(x²) – 2xy + 1]dx + [sin(x²) – x²]dy = 0

A: The solution attached :

Q: 3x*y+2x +y² +5 = cos(2x)+5x

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Q: 1 3 X° cos 4- x2 dx + 2 2

A: We will find the value of definite integral as following.

Q: 2 cos Vx = cos (2x-1) 0<xs1

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Q: 2. cos x dx - 67

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Q: solve the nonhomogenous equation y''' - 6y' = -cos(x)

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Q: a²-x2 6- Sº, S dy dx -Va2-x2 7- Sx? cos 5 x dx

A: As per bartelby guidelines we have permitted answer only one question if given more than one…

Q: (6secx cos x dx :

A: Put secx = 1/cos(x)

Q: X cos-dx x cos 3.

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Q: y" – 2y' + y = [-6x – 8] cos(2.x) + [8x – 11]sin(() 2x) %3D

A: We have to solve the differential equation y''-2y'+y=[-6x-8]cos2x+[8x-11]sin2x.

Q: x – sin-'(x). dx. /1 – x²

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Q: (b) Determine cos(x²) 2x dx by using substitution method.

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Q: dx 2x2+8 dx -9x2+6x-2 e 2X sin(e2x)dx cos²(e2x)+3

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Q: )Evaluatef 4x cos(2-3x) dx

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Q: dx 9. 2- cos X

A: To evaluate :