Solve: COS x y'dy +ye' sin x dx = 0.

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A: To find the derivative of the given function y  = cos(x)/(1 + sin(x)).Use the quotient rule for…

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A: Please refer the attached image for complete solution.

Q: sin3x dx 1+cos3x х dx x+4

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Q: 2. y = (cosx)(sin5x)

A: We will use product rule of differentiation to find the first derivative of this function. We will…

Q: 1 cos(sec-x) dx 2/V3 xVx²-1

A: Let's find.

Q: 2- cusx dx COSX Sinx +2 Sinx t5

A:

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: Find the coordinates of the point on the graph of y = 8 sin x+4 cos (2x) + 14, 0 <x<5, where the…

A: Consider the given function, y=8sinx+4cos2x+14 The slope of the tangent line on the given curve will…

Q: dx sech x (3 +5 sinh x)

A: Please see the explanation below.

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

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

Q: Differentiate y=(1-cosx)/sin2x

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Q: Solve S(cosa{x – +)<(1 + +) dx -

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Q: Solve: cosx + sin x + 1 = 0, 0 sxs 27.

A: Given: cos2 x+sin x+1=0, 0≤x≤2π

Q: Ssin | sin" x cos" x dx if find

A: Odd function :- When the function is of the form f(-x)=-f(x) i.e., when the value remain same but…

Q: 1. cos(xy) + secy = 5

A: Differentiation is the process of determining the derivative also known as the derived function. one…

Q: solve sin2x dy/dx-y=tan x

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Q: 3. J sin53x dx. 4. J tan 2x sec22x dx.

A: ∫ax+bn dx=1aax+bn+1n+1+C

Q: 1- 1- (Sin (coshx) sinhx dx

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Q: I3Jsin'x cos x dx .6,

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Q: 3 sinx 19. dx V1-x²

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Q: Solve (cosx)dy = (sinx)dx

A: The objective is to solve the expression cosxdy=sinxdx

Q: Find az when yz+x In y = 2.

A: Use implicit differentiation

Q: sinx(tan(x/2))-sinx=0

A: sin x tanx2-sin x=0

Q: Solve to Find if cscx – ) dt = 4 – y? tanx sinx+1. dx

A: Here we have,  a) y+∫xsecx1sint+1dt=xy b) cscx-∫tanxxy1sinx+1dt=4-y2

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

A: 1) Evaluate: ∫sin42x-1cos32x-1dx

Q: 23. cos (3z + 4) dz 25. sec2 (3x + 2) dx

A: A

Q: Solve for the derivative of y=ln ln [cos2(3x)] With the answer -6 tan tan (3x)  Show solution.

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Q: Solve sin - () 2 dy = x + y

A: We need to use substitution method to solve this differential equation

Q: [17 sin³ x costx dx 5.

A: Given: I=∫17sin3xcos4x dx. To evaluate: Value of integral I.

Q: how to solve this equation using variation of parameters.    y'' + y = tanx

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Q: | sin-1 3x dx

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Q: solve sin2x dy -y=tanx dx

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Q: integrate [(x csc^2 (2x) - x cos (2x)] dx

A: Given problem:-  ∫ [(x csc2(2x) - xcos(2x)] dx

Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 1. y = Arcsin(- Vx²+4

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Q: Evaluate sin (4x) cos -2(4x) dx. | sin (4x) cos -2(4x) dx = O

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Q: sec“ x (Vtan3 x +1) dx (Vtan3, Px+1) 4

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Q: Va2-x² Y=Arc sin- + а

A: Solution-

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Q: Find dy/dx if sin-(4y²) = 8x² – 5y3 Answer: Find dy/dx if tan- (xy²) = 3x² – 5y² Answer:

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Q: 2. S CoSx+sinx-1

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Q: Differentiate.   y =  Sin -1(ex)

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Q: Explain how to find ∫ tan15 x dx without actually integrating.

A: ∫tan15x dx=∫tan13x tan2x dx=∫tan13x sec2x-1 dx   ∵sec2x-tan2x=1=∫tan13x sec2x-tan13x dx=∫tan13x…

Q: Integrate:  ∫ cscx cotx − sec^2 x dx

A: Solve by integration

Q: Differentiate y= x2  sinx

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Q: fcox In(sinx) dx= fu du cotx In(sinx) dx = u du

A: In this question we substitute  u=lnsinx .

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Q: SOLVE: (y cosx +2xe")+(sinx +-ng'= 0 COS X

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

A: