d²y + 4y = x² sin 2x dx2

Q: 2 sinx d x V1-2cosx

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Q: Find if x2y - sinx - cos y dy dx O dy da 2xy x² COS sin y 10.

A: Given: x2y-sinx-cosy=10. Now,                x2y-sinx-cosy=10Differentiating both sides wrt…

Q: Solve d²y dx² - cot x dy-sin² x.y = cos x - cos³ x. 2 dx

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Q: dx (2) 3y sin x 2xy cos x = 0 dy (3) 3x²y² + 2x³y -= 0

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Q: Solve dy 2 dx - dy + 2y = 7 cos x + 5et dx -3-

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Q: ∫ 2cos^2(x)sin(3x)dx

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Q: 1. [ (6x² – 2x+3)dx sin(2x)dx 3 2. 3. S2 8 dx X+2

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Q: COS V4- x2 dx -2 1/2

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Q: 4si 2xcos²x dx sin2xcos2x

A: It is given that,     ∫4 sin2xcos2xsin2xcos2x dx We have to evaluate it.

Q: sin x dy 2. dx 2у x2

A: In this question we have to find the solution of the given differential equation.

Q: 2cosx dx 2 5- fn 1+(sinx)? π

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Q: (b) S tan3 x sec² x dx c) S sin³x cos5 x dx

A: The explanation of the solution is :

Q: 4 f sin(5 – 6x) sin (6x – 4)dx -

A: Here limit are not given so we integrate only without using of limit.

Q: Solve - s d²y + 6y = 2 sin 4x dx | %3D .2

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Q: 4. X sin (x) dx VI-X 1-メ-

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 5y + sin y = x²

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Q: | – (3x² sin x + 2) dx In r dx Je

A: Since, you have asked multiple question, we will solved the first question for you. If you want any…

Q: find dy / dx if y2 - x2 - sin xy = 0.

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Q: y = sin(3 – 4x)" %3D

A: Apply the chain rule of derivatives, If y = f(g(x)), thendydx=d(f(g(x))d(g(x))×d(g(x))dx

Q: Integrate (sin1/2)(x)dx

A: The given integral is ,∫sin12x dx=∫sinx2  dx

Q: Solve f 4x cos(3x) dx using Integration by Parts.

A: This is based on integration by parts

Q: Evaluate (a) 2. Sinx+ X=X (1) Sinx dx T+x²

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Q: find dy/dx 27. y = 4 tan (x3/3)         28. y = sec (x2 - 1)

A: ddx4tanx33Take the constant out:  a·f'=a·f '=4ddxtanx33Apply chain rule:=sec2x33ddxx33=4sec2x33x2

Q: d cos 2x – x³ i. dx 3 + tanh x

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Q: V sin2(x32 - 1) dx, with u x32 - 1

A: Consider the integral ∫(√x)sin2 (x3/2 - 1) dx.

Q: a) Find for 5x² – x³ sin y + 5e*y = 10 dx

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Q: 2 | (sin³x cos x + sinxcosx)dx 7/2 π

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Q: π/2 sin3 (4 ) αθ - π/2

A: To evaluate the following integrals

Q: 5. J sinx cos²x dx V1 − cosx -

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Q: 2x+5 dx = AV7- 6x - x2 + B sin - (**)- 1. Vア-6xーx2 +C

A: ∫2x+57-6x-x2

Q: Solve x3sec2y dy/dx+3x2tan y=cos x

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Q: 10. J(3x3 — 5х + sin3x) dx -

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Q: 7. 2r tan y dx + sec² y dy = 0

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Q: (T/3 4 sinx -dx 1-4cosx 1-

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

Q: 3 sinx 19. dx V1-x²

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Q: 3. X sinx eas x dx 2.

A: To find out the integration.

Q: 1 sin-1x + - y)dx + sec¬1xdy = 0 xVx2 – 1

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Q: 1. Ssin (2x-1)cos (2x-1)dx

A: 1) Evaluate: ∫sin42x-1cos32x-1dx

Q: Evaluate 1- cos X dx. 2 1- cos x dx = %xp 2

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Q: 2cosx dx Sr 1+(sinx)²

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Q: solve sin2x dy -y=tanx dx

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Q: 3. f sin³y(2-3cosy)² dy

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Q: 1. D² {Sin ² x 3 2. JD²-15² √2e²x3

A: Here D is the differential operator. D=d/dx

Q: Se²x+lnx² sin x² dx = +fe²x co 2x cos x² dx

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Q: dx b) sin 2x sin x dx (3x + 2)²

A: we have to integrate

Q: 2cosx dx 2 1+(sinx)²

A: Please refer the attached image for complete solution.

Q: Solve y dy + 2y = xe* + sin 2x 3x - 3 | %3D dx dx

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Q: 4. c) Integrate x² sin(4x)dx.

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Q: SVx² + 10x + 25 dx. (cos4*x – sin4*x)dx dx

A: