11 csc²(3x) cot(3x) dx =, (Use Substitution Method) 11 11 +C 6 sin (3z) 6 11 11 +C 6 sin (3z) 6 11 11 +C 6 cot2 (3x) 11 11 +C 6 cos (3z)

Q: 1 -dx = /8-(2x+5)² o įsin- (2*) 2x+5 + c V8 2x+5 sin-1 + c 8, tan- ( V8 2x+5 + c o ţtan" (2*5 ) + c…

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Q: sin(x)cos(2x)sin(3x) dx D sin(6x) sin(2x) sin(2x)cos(4x) + + ++ C 24 8 sin(3x)cos(3x) 12…

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Q: + 5x + 6 cos x + 2)dx = e – x + cos a + 2 + c - O 3e* + x³ + 6 cos x + 2x + c 3et + x + 6 sin x + 2x…

A: We need to evaluate the following integral I = ∫3ex+5x4+6cosx+2dx

Q: 4 Se + 5x* + 10 cos x + 2)dx 5e" + x° + 10 sin x + 2x + c 5et + x 10 sin x + 2+c - et x° + cos x + 2…

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Q: cos 2x he ƒ -dx is 4+sin 2x {A} In|4 + sin 2x| + C {B} In|4 + sin 2x| + C {C}(4+sin 2x)² + C {D} -(4…

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Q: gral. cos 7x cos 4x dx ㅇ응 cos 3x + 숲 cos 11x + C ㅇ sin 3x + sin 11x+C 1 sin 3x - sin 11x +C

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Q: If e /2i =sin2 then z = /21 - 2 In(sin2) + 4kTt – 2i In(sin2) – 4kt | 2i In(sin2) + 4k T - 2i…

A: We use the identity e^(2πki)=1 and by tanking ln both sides and then calculate.

Q: -3x cos 2x da A) - cos 2x - 3x sin 2x + C B) - 2x- sin 2x +C s 2x - sin 3x + C D) - cos 2x - sin 2x…

A: Since you have posted multiple questions . As per the guidelines we will solve the first question…

Q: 7. y = tan³ (2³) (A) 3x² sec(2³) tan(x³) (B)-3x2 sec(³) tan(x³) 8. y = cos(5x) (A) sin(5x) (B)-5…

A: Topic = Derivative As per guidelines, At a time only three sub-parts of a question can be answered.

Q: | cos(Vx) dx A 2 Vx sin (Vx) - 2 cos ( Vx) + C C 2 Vx sin x (Vx) - 2 cos (Vx) + C B 2 Vx sin (Vx) +…

A: To evaluate: I=∫cos xdx Substitute x=u⇒12xdx=du⇒dx=2udu So, I=∫cos u 2u du=2∫u cos u du

Q: S A. sinxcosxdx √esc²x-1 2 B. 7 COS X 7 5 COS X 5 5 cos³x x + C X 5 7 COS X 7 +C C. D. sin7 x 7 5…

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Q: sin(4x) cos(2.x) dx n (2x) sin (6x) cos (2x) cos 2. ()= 4 'cos (2x) cos (10x sin (2x) trts 10 (e)…

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Q: f cos(x³) x² dx. O 1 ¹ cos4 + c 4 1 3 sin x²+ C 1 1 ¹ cos4 + c - 4 -3 si sin x³+ C

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Q: sin³ (cos(4) dx 2 32 Ⓒcos A COS 35 32 B 35 32 Ⓒ-3 cos (4) C 32 D 3/7/7 C (4)[-5cos (4)+7] 5³ (4)…

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Q: |5x sinx dr = - 5x cosx +5 sinx +c OA. 5x cosr +5 sinr +c В. None 5x cosr - 5 sinx +c OD.

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Q: tan x-7 3. Differentiate. y = secx Select the correct answer. dy bl dx a) = 7 cos x + sin x = cos x…

A: Note that derivative of sinx is cosx and derivative of cosx is -sinx

Q: ƒ cos(x³) x² dx. 1 ¹ cos4 + c 4 1 WIT 3 1 -| sin x³+ C 1 ·cosª + c 4 4 -3 sin x³+ C

A: Topic = Integration

Q: cOs x dx |(sin? z + 4)%/2 1 sin x sin x cos x 1 cos x +c +c 16 vsin ²x + 4 48(Vsin ²x + 4 16 Vsin 4x…

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Q: 7. y = cos`x sin'x %3D 3 A. – 4 cos x sin x B. – 2 sin sin 2x 3 2 C.- 4 cos´x + sin' D.- 2 sinx cos…

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Q: sin (21 + 1) dt J cos² (21 + 1)

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: sin(1) dt Using an appropriate substitution, evaluate: [2+ cos(t)]* A +C 3[2+ cos(t)]3 3 B +C [2+…

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Q: Q.3) 3+4x+20 dx = a) Q.4) f sin5x sin4x dx = tan-(+) 4 a) = (cosx - cos9x 9 cos9x c) (cosx +°%$*) +…

A: ∫1x2+4x+20dx∫sin5xsin4xdx

Q: 1-cos 3x +C 3sin 3x dx 2. 1+ cos 3x

A: We have to prove given integral.

Q: S 4x* sin2x dx A (2xª + 6x² + 3) cos 2x + (4x³ + 6x) sin 2x + C C (2xª – 6x² • 3) cos 2x + (4x³ –…

A: Integrating by parts : ∫u.v dx =u∫v dx -∫dudx∫v dxdx dxndx=nxn-1 ∫cos(ax)dx =1asin(ax)+C ∫sin(ax)dx…

Q: Integrate 0 1 S √1 1-4x2 dx using a trigonometric substitution. sin-¹ (2x)√1-42²+ C 0 1 -sin-¹ (2x)…

A: The given integral is sqrt(1-4x2).

Q: St' sin(2t*)dt (sin(2t*) - 2t*cos (2t*)) + C (sin(2t*)-2t cos (2r*)) +C 14 1 (sin(2t*)-2t cos (2t*))…

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Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…

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Q: | cos(V) dx 2 Vx sin (Vx)-2 cos (Vx)+C C 2 Vx sin x (Vx)-2 cos (Vx) + C 2 Vx sin (Vx) + 2 cos (Vx) +…

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Q: у" + 25у %3D 0, у(0) 3 6, у'(0) 3D —4 Y(x) = | 5 cos( 5x) – sin(5x) sin (5x) x

A: We have given differential equation y"+25y=0 with initial conditions y(0) =6, y'(0) =-4 We have to…

Q: 17. (D4 + 2Dz + 1)y = 5 – 3x² a. y = (C1 + C2x) cos x + (C3 + C4) sin x – 3x² + 17 b.y = (C, + Czx)…

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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: sin 4t sin 2t dt 1 sin 6t + C 12 cos 6t + C sin 2t + B) sin 2t 1 · sin 6t + C 12 D) 1 sin 2t + C 12…

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Q: sin dx 32 cosS 35 4 Ssin +2 +c cos () • 32 cos + C 32 -cos 32 cos + C 7 4 32 cos 35 즐)-Scos()+기+C

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Q: /² sin sin ( π/4 x² dx (x²+4)5/2 (Use trigonometric substitution) fe2x+Inx² sin x² dx = = Find f…

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Q: Sræsin(x³/2)dx= cos(x3/2) + C A 2 B) -을 cos(x3/2) +C ©-3/2 cos(x3/2 ++ C) C 2 D /xcos(x³/2) + C

A: Given: Let I=∫x sinx32 dx To Find: To evaluate the given integral.

Q: y sin 2x + cos 2y = ax Find y' a – y cos 2x y% = sin 2x – sin 2y а - 2у сos 2x y sin 2x – 2 sin 2y…

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Q: S sin*x cos³ x dx C sin5x sin'x + C 7. sinx sin'x + 5 sin x cos'x + C 7 D sin5x cos'x + C 7. 5

A: We know that ∫xndx=xn+1n+1Also, d(sin(x))dx=cos(x)

Q: sin 2t cos 2t dt 1 +3 cos 4t

A: Integration is the process of finding the anti-derivative function of the given function. The…

Q: 6. ans. -2cos(1/2)x + C 2 Scos3xdx 7. ans. (1/3)sin3x + C . Stan2vdk 8. ans. (1/2)In(sinx?) + C

A: As per the company guidelines we can solve first three parts. I hope that the given solution will…

Q: 30 csc (3x) cot(3x) dx (Use Substitution Method) 30 30 + C 6 cos² (3x) 6 30 30 + C 6 sin²(3x) 6 30…

A: Given that  I=∫ 30csc23xcot3xdx We need to substitute the appropriate value so we can solve it…

Q: 6 (A) /₁ √== B)/ -x/4 D) dx = tan* (x) sec²(x) dx = C) [rea *² x² ex dx = E) 2x cosh(x²) dx = F) /…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first question. If you…

Q: (2 - 3 sin 30 + y) dy- (9y cos 3p- p+1) do 0, y (0) = 2 Dy+4y-6y sin 3p+ q-20= 12 O y-y+9y cos 30- p…

A: We have to find

Q: J (sin 3x)² = sin 3x xp- sin 3x CO = sin 3x xp- sin 3x On simplifying further, y2 (x) = cq sin 3x /…

A: In this question , constant is to be included in the last solution of the differential equation.…

Q: 3) [~x cos² (x3/2 - 8) dx , A)sin (x/2 - 8) + C 1 = x3/2 – 8 3) 1 B) a32 - 8) + sin 2432 - 8) • C D)…

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Q: e sec(3x+2) sin(3x+2) dx Evaluate cos² (3x+2) -3e sec(3x+2) + . O 1 ,sec(3x+2) + C 3 1 ,sec(3x+2) 3…

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Q: Q.23) cos Q.24) cos(sin ¹x) = 24 sin11x) √1-1 d)√1-x² b) (sinx+1)+c 11

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Q: ∫0π/2[√(cos3x) sin3xdx]

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Q: 26 csc (2x) cot(2x) dx (Use Substitution Method) 26 26 + C 4 sin (2x) 4 2 26 26 + C 4 sin? (2æ) 4 26…

A: Integration.

Q: f5cos(1-5x) dr = O - 5sin (1 – 5x) + C O -sin (1 – 5x)+ C 一 sin (1 5x) + C 5 - O sin (1 – 5x) + C…

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