/2 | cos(r)e sin z dx O a. el O b. e sin 1 C. 1—е 1 O d. cos 1

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A: Solution of the problem as follows

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A: To find the value of given ∫0π23cos2xsin3xdx

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A: We can solve using first order differentiation (using chain rule)

Q: et Cosnx dx = 1 (-1)"+1 an تكامل مرتين بالتجزئة, (e- e( - | TI 1+n bn 1 (-1)"+1 ex cosnx dх 3D تكامل…

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A: Use seperation of Variables.

Q: I. Obtain the general solution of the following: D. (3D2 + 12)y = tan x E. (D2 − 3D + 2)y = cos…

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

Q: (c) Show that e* sin(x²)dx < e – 1.

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Q: Find the most general antiderivative of the function.

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Q: Take the derivative of this integral.

A: Given

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Q: (a) L{t+ sin 4t – e cosh nt} -

A: As per our guidelines, we are supposed to solve only first question.

Q: -) sin A = d.) cos M = 34 25 hy 16 24 30 K e.) sin L = f.) tan G = M. 7. K 8. 15

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

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A: I understand that we need to find the derivative of this function as nothing is mentioned

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Q: se 16) F(s)=- s+4 cos(21) Ans. f(1)= elsewhere

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A: Given that  L(cosat)=s/(s^2-a^2) To find the condition is true or false

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Q: 8. (e' + 2) sin x dx – e' cOs x dy = 0 Ans. (e' + 2) cos x = C dy et-y +x?e¯y Ans, e = e* +: +C 3 9.…

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: If y= cot"+ tan-1x?), then dy dx x2 Select one: 2х + 1+x*' 1-x4 2x O a. 2x O b. 1+x' 1+x? 2x Oc. 2x…

A: All given options are wrong. See the attachment

Q: dy 6. For parts (a) and (b) of this question, find Simplify your answer. dx (a) y = e® Inx

A: Derivative: y=tanx1-cosxddx(uv)=v.ddx(u)-u.ddx(v)v2

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A: solution.

Q: 1. Please answer the following questions. a) [x-In (4x²) dx b) ſe* *. cos (2x) dx c) [In (x² +2) dx…

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A: We will evaluate the given integral in the following step.

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A: Given

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Q: D. ( [ 3° cos"(5t) dt sin(z)

A: