dx (iii) f 1 dx sinh x (iv) S (x-3)Vx²-6x+8

Q: A-f cos (x)sin³(x)dx e*cosh (3x) B-J cosh(x)+sinh(x)

A: Here we use use substitution method to evaluate the given integral.

Q: sinhx dx=.. ...+ C Select one: coshx, coshx O cosh x-2- (1-cosh?x) (cosh2x-1) 3. cosh x cosh5x X. O…

A: Given: ∫sinh5xdx

Q: STox -x* dx 2.

A: To Evaluate: ∫6x-x2dx

Q: 8 3x -dx 3 3 V 2 – x 2 -

A:

Q: 14.1 dx V16-x dx 15. . Vx -1

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

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Q: (ve-2x + y²) dx - e-2x dy = 0 6. (ye

A: We need to identify the given first order differential equation as homogeneous, Bernoulli, linear…

Q: ://v². dx √1-x² dx √√2. x√x²-1 (ª (¹² - 31/₁) dr (1. 25. 27. 29.

A:

Q: dy (у+1)(х-2)(у-3) dx (х+1)(у-2)(х-3)

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Q: x-2 dx x + 2

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Q: y' %3Dх (1 — у?) 2 2ху — 10у —х+5g- 0 ху +5у + 2х + 10 2х + 3 -dx + dy = у — 6

A: given differential equations are first order variable separable differential equation. We will first…

Q: 2. S (3x- 12) x'dx (3х I dx 2.

A:

Q: intergral x^e^3x^2+1 dx

A: I=∫xe3x2+1dx Then let I1=∫xe3x2dx, I2=∫1.dx Then, I2=x Let fx=xe3x2

Q: [4] S (x + )´ dx [5] S cos²(2x)dx X. V1+x3 [6] S- dx r-2

A: To evaluate the integration of the following.

Q: 4. S dx 9-x x2-1 dx 5.

A:

Q: sech? (In x²) 15. f x/6 tanh (In x²) – tanh² (In x²) dx

A: I = ∫ sec h2 (ln x2)x6tan h(ln x2)-tan h2(ln x2)dx=∫ sec h2(2ln x)x6tan h(ln x2)-tan h2(ln x2) dx=∫…

Q: (sin'x-4)dx- tanx dy=

A:

Q: cosh 3x-1 S - dx 2

A:

Q: | sin x (3cosx)dx 2: VZ 3x dx V1- x4 3:

A: SOLUTION-

Q: cosh x sinh x dx 2 (cosh x + 3)

A:

Q: 2x (x-a)² dx; a is constant

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Q: f(x) = cosh(sinh(x²))

A:

Q: (y-sinx) 3. Solve the D.E. dy + dx = 0.

A: We can solve the given differential using integrating factor.

Q: (e² sin³(2r) (d) y= ln 2x2 + 1

A: Given, y=lnexsin32x2x2+1 derivate both side and find dydx dydx=ddxlnexsin32x2x2+1…

Q: sinx

A:

Q: 3x dx V1-x

A: Integral is given

Q: x 3 X 14.J. J16-x 2 -dx V16-x² dx 15. Vx -1 4

A: Use integration rules

Q: 7. y= (x²-1) sinh (x+1)ª 8. y= sech (1-x³) 9. y =- tanhx

A: Answer (7): The given function is y=x2-1sinhx+14 using product rule in differentiating above…

Q: 1. dx/(x - 1)³ 2. (1-x²)² dx 3. f (x² - 1) x dx

A: The first three integrals are: 1. ∫dxx-13 2. ∫1-x32dx 3. ∫x2-1xdx Here we use the integral formula:…

Q: dy Зx+2у-5 3) dx 2х +у -3.

A: The given differential equation is dydx=3x+2y-52x+y-3.

Q: e-V2x sinh x sin x x dx

A:

Q: (sin (x))2 dx V1-x2

A: The given integral is

Q: x² +3 -dx +8x + 25 1) Integrate |

A: Solution: The objective is to find the value of the given integral

Q: V1-x² 1–x2 dy dx -1 . J-V1-x²

A:

Q: (3 sinx-sin³. 9. lim x3 А. О В. 1/4 С.4 D. DNE

A: We will find the limit

Q: x - 7 Integrate dx. x2 – 2x - 3

A: NOTE: Refresh your page if you can't see any equations. .

Q: 10. f(3x - 1)(x - 1) dx

A: The given integral is:∫-113x-1x-1dx

Q: cosh x dx е e- 2х

A: Given integral is ∫coshxe-2xdx

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Q: x +3 b. dx x2 - 3х - 10 с. x³ In(x²)dx at LKnow Chart part 2

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Q: ODE (3x-2y+1) dx+ (3x-2y+3) dy=0

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Q: 2 1 dx V4-x2 1 dx xInx ーX xe*dx 1 8. 8.

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Q: | (e-x + vx)dx 1. 2. x²)dx

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Q: 18) fvī dx 19) f se'de 3e dx 20) (3x - V5x + 2) dx

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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: dx 1 xii. dx V3-2x-x² хі. Vx(x+1)

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Q: dx 4) S JaNx - 6) dx 5) N-x2, 4x + 5 6) S tan x dx Vsec2 x - 4

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Q: V1+ sin (x5) e-y 2(Vx- 1) f-- cos {sin(2x*)} x-2 x2+3x

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Q: 3. dx V3-x

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Q: 3. dx 6X dx VT-x2 1-x² Et2

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Q: | 4x sech x2 tanh x2 dx A) - 2 sech x² + C (в) 2 B sech x2 + C sech x2 +C C 2x D) 4 csch x2 + C

A: