For the function f(x) = 2 sec (2x) tan (2x) + sin(x) + cos(x), find the most general antiderivative F(x).

Q: Find two antiderivatives of f (x) = cos x. Then determine the general antiderivative.

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Q: Find the differential of the function y = f(x). 2x2 + 5 f(x) = X + 5 dy = %3D

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Q: Find the antiderivative of f(x) = sin^2x

A: Antiderivative=∫sin2xdxsin2x=1−cos2x2So,∫sin2xdx=∫1−cos2x2dx=12∫1−cos2xdx=12∫1dx−∫cos2xdx=12x−∫cos2x…

Q: Use the intermediate Value Theorem to show that between x = 0 and x = 1, the function f(x) = 3 sinh…

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Q: find the antiderivative F(x) of f(x)=x^2+sin(x)+3 with F(0=8

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Q: Find the third derivative of f(x) = ³/15z + 1. f"" (2) - ab a b √a |a| π sin (a) 2.

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Q: Find f(x), the most general antiderivative of the function: f" (x) = 18x – 3 sin(x)

A: Explanation of the answer is as follows

Q: Let y = f(x), where f(x) = 7x³ + 3x. Find the differential of the function. dy = X

A: The differential of y is the derivative of the function times the differential of x,

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = x/9 – x²

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Q: se C for the constant oT integration.) (7 cos x + 3 sin x) dx

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Q: f(x) = 9x3 + 4x.   Find the differential of the function.   dy =?

A: Given , y=fx where fx=9x3+4xwe have to find the differential dy

Q: Find the most general antiderivative of f(x) = -3e" + 10 sec2 (x), where - < x < 2 Note: Any…

A: According to the given information it is required to calculate the antiderivative of the function:

Q: Find the most general antiderivative of the function. f(x) = + 3 cos x

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Q: Find the differential of the function y = f(x) . f(x) = (5x² + 7)/3 dy =

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Q: B) Find for the Implicit function: dx x2 - sin(xy) + y² = 5xy

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Q: Let y = f(x), where f(x) = 6x2 + 3. Find the differential of the function. dy =

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Q: (3) Integrate using an appropriate substitution 2e- -d.xc e + 3 x-

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Q: Use the appropriate form of the chain rule to find the derivatives. w = 12x2 + 12y² + z²; x= p sin o…

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Q: Some elementary functions, such as f(x) = sin(x2 ), do not have antiderivatives that are elementary…

A: let ∫x-necxdx for n a positive integer and c a non zero constant is non elementary since…

Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

A: Given that

Q: Let y = tan(2x +5). %3D Find the differential dy when x = 5 and dx 0.4 Find the differential dy when…

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Q: Find the most general antiderivative of the function. ( Use C for the constant of the…

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Q: Let y = f(x), where f(x) = 3x+6/x+6 Find the differential of the function. dy =?

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Q: 3. x cos x dx

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Q: when

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Q: sin x dx COS x

A: Indefinite Integration Substitution

Q: Find the antiderivative of f(x)=cos(3x)

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Q: of

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Q: Find the differential dy of y = tan x for x = π/4 and dx = −0.1.

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Q: 11) Find the antiderivative: f -3+6√x³ √√x dx

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Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

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Q: If f'(x) = 5x*, what is f(x)? (Use C for the constant of integration.) f(x) =

A: To find the integration

Q: cos xdx (vii) S 5+sin2 x

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Q: 4. For the given derivative, find the antiderivative that satisfies the indicated condition. f '(x)…

A: We have to find the anti derivative of the function or we can say that we have to integrate the…

Q: Find the differential dy for y = x2 - 4x + 6, then evaluate it when x = 2 and dx = 0.1

A: Differentiate the given curve y=x2-4x+6 w.r.t.  x use the power rule of differentiation i.e.…

Q: Find the general antiderivative of the given function. sin( x/7π)   and  sec2(5x) + sec2 (x/3)

A: GIVEN DATA : Function sinx7π and sec25x+sec2x3        TO FIND : Anti derivative of the function…

Q: Let y = tan(3x + 8). Find the differential dy when x 5 and dx = 0.4 %3D Find the differential dy…

A: First differentiate then put the values

Q: Find S x cos x dx by using integration by parts.

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Q: Determine the most general antiderivative:  f(x) = sec x tan x-2e^x

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Q: Find a function whose 2nd antiderivative is f(x) = tan(x) + 4x+1

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Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

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Q: Use the appropriate form of the chain rule to find the derivatives. 5.x2 + 5y2 + z²; x psin ф сos 0,…

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Q: Find the differential dy of the given function. sec² x y x² + 2 sec 2x (2x²tan x + 4 tan x-2x)…

A: This question is based on quotient rule

Q: Find the antiderivative of the function f(x) = - 4 sin (4x) when C = 0. The antiderivative is

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Q: sinh x – 1 dx cosh x

A: The given integral,        ∫sinhx-1coshxdx

Q: Let y = 3x² + 8x + 3. Find the differential dy when x = 1 and dx = 0.2 Find the differential dy when…

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Q: Find for the Implicit function: dx x² – sin(xy) + y² = 5xy

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Q: Find the general antiderivative of the function f(x) = +3 sin x - : 1 1+x?

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Q: Find the most general antiderivative of f(x) = sin x cos x .

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Q: Find the antiderivatives |x In(x²) dx + sec? x dx CO X dx sin5

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