Integrating Hyperbolic Functions 13. Evaluate, | sinh* x cosh x dx 14. Evaluate, dx xVx? +16 15. Evaluate, x2 16. Prove that, cosh-x = In x + Vx2 - 1 for x 21 Integrating by Partial Fractions 17. 4x2 – 21x dx J (x - 3)2(2x + 3) 3x2 - 4x +5 dx (x - 1)(x2 + 1) 18 19. 10 dx (x + 1)(x² + 9)2 20. x*-2x2 + 4x +1 x3 - x2 - x + 1 xp

Q: 1 Find the derivative of f(x) = V7+4x2 - 5.x2 +9

A: we apply chain rule in the first part and division rule in the second part

Q: -2 S₁² S₁² (²x²y^² + 2 (2x²y-² + 2y) dy dx 1 1

A: Given- ∫12∫1x(2x2y-2+2y)dydx To evaluate the given integral.' Here we will use the following…

Q: Find f. f"(x) = −4+ 8x - 12x², f(0) = 4, f'(0) = 12 (Prob. 1,

A: Consider the derivative function and initial conditions, f''x=-4+8x-12x2,f0=4,f'0=12 The objective…

Q: 3) f(x) =9x/チxー3 %3D

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Q: 14) fx In(4x) dx

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Q: Differentiate. V(x) = (3x³ + 3)(x* – 2x) V '(x) =

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Q: dy + ydx = 3x²y?dx, %3D

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Q: solve D'+)y = carec x by seduetion of Oxdex

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Q: (1/x 15. h(x) = Sy sin't dt

A: hx=∫21xsin4tdt

Q: Differentiate. y = In (4x² - 7x+9) y'=0

A: The function is The aim is to find the derivative of the function

Q: do implicit diff for thi with respect to x (xy)^(1/2) = 4 + x^(2)y

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Q: -3 Now, g'(x) = 8 Define f(g(x)) = such that f(x) = -12 -12 Rewrite the given integral in terms of…

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Q: dy If y = ( a² +1) (x³ + 3) dx %3D O 5x^4 + 3x^2+ 6x 6x^3 O 2x + 3x^2 O 2x^2 +2x+ 3x^5+9x^2…

A: Question 1,Given,            y=x2+1x3+3To find: dydx

Q: S2(x* +1)e** dx . -5x t³ -9 -dt . 2t +3

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Q: Show /x^ In х dx xn+1 ((п + 1)In x — 1) (п+1)2

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Q: 2 1 dx (3+5x}

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Q: find dy/dx of x^5y-xy^5=1

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Q: х — х* - 3х - 2 X | dx x* - x'+ 4x – 4x 3

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Q: General solution

A: We have to find the general solution of given differential equation.