sin² 2 (KTT) сс 2 Σ (***)_ ~*(+)) k4 k=1 8k

Q: T² 2 / (x + 1) (2² + 1) dr. Evaluate

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Q: Question -2x2 + 4x dx J (x² + 1)(x² – x)

A: Given: ∫-2x2+4xx2+1x2-xdx

Q: d/dP (11 - 3P)

A: We have to find the differentiation of the function: d11-3PdP We know the formula of…

Q: S(x + 1)(2 – x)° dx 7(2 - x)* - (2 - x)* +c 7(2 - x)* -(2 – x)* +c 3. (2 - x)* +(2 – x)* +c 금(2-x)*…

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Q: (3) Find 125 * dx I- e

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Q: 10*(100* + 1)dx

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Q: [2x*dx (Ans. 3 2 x' +c ); (xi) J3x°dx - 3 In\x)| 3 |3x'dx (Ans. (Se* –x? +2)dx , (x + 0) (x) x' +c);…

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Q: (4) VL1, L2 ((L1 UL2)* = L₁* U L₂¹).

A: This is always True

Q: find f'tx) w/

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Q: ∫x+2x√3−6x32x  dx∫x+2x3−6x32x  dx = ∫3sinh(lnx2)  dx∫3sinh⁡(ln⁡x2)  dx =  ∫69+x2  dx∫69+x2  dx =

A: As per bartleby guidelines we only give first three question answers.

Q: det(A) Show that det(AB-') = %3D det(B)

A: Consider, Let A and B be the two n×n matrix, Now Consider, detAB-1 We know that the theorem, Let A…

Q: (d) dx (e) S,(4x + 2)5 + (6 – 4x) dx (f) S,' 4x3 – 3x* dx

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Q: y'" — 7y' — бу = 0

A: Solution :- This higher order differential equation can be solved simply by using complementary…

Q: 0. Reciprocal Substitution (x´ - x')"3

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Q: pk Ph (x)=k! T(m-k+1) (k+m+1) m X \x X

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Q: (4³ + 6)%,' = x^(,5 + 6)5 y

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Q: F"(x) = 6-18x, 0) = 9, 2) = 11 F(x) = 4x -3 +Ox+9 3p3 O Tyne h

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Q: d? -(sin-'(x²)) dx2 2– 4x4 A 3 2– 2x4 B 3 2+2x4 3. 2+4x4 D

A: Here we have to use the concept of derivative

Q: 3-J (х* + 2х 3) dх

A:

Q: sec (2x) dx (tan 2x-4)"

A: We have  ∫sec2(2x)tan2x-43dxLet  tan2x=u    diff. w.r.t x we get2sec2(2x)= dudx sec2(2x)dx=12du now…

Q: how

A: Que seems some data missing. Though I have simplified the given expression as much as possible.…

Q: (:' } - 8) zp - Vz(z – 2)

A: We use the difference of cube formula for numerator

Q: + If x? = x-y then, y *+y

A: Given  x2=x+yx-y first we multiply each side by x-y x2x-y=x+yx-yx-y     by dividing  x-y from x - y…

Q: E (3x(9 ^ b) V Jaæ(p ^ 0)) = 3x(p A (4 V 0))

A: To prove ⊢(∃x(φ∧ψ)∨∃x(φ∧θ))≡∃x(φ∧(ψ∨θ)) Here we have to use existential quantifiers i.e. notation of…

Q: find dy/dx 4x -x 2x 23) y= Sin- +x².Sec 2-x + 2x.Sec) 2 (ans.: (2-2»N(2-x² - x* 4 4

A: To find the dy/dx means y' of the given function

Q: 는(csc-1(324)) = d SC dx

A:

Q: Solve for x in the equation 3* + 9* = 27* What is the sum of the coefficient of (x + y −z)8 What…

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…

Q: The f ²-3)³ dx is equal to x2

A: Given: I=∫x2-33x2dx For evaluating given integral, first we simplify given expression then integrate…

Q: List all intervals for which there are possible unique solutions (t-5)x''-ln(t)y'-y=et

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Q: 6. dx = x + 4x + 5 (A) arctan(x + 2) + C (B) arcsin (x + 2) + C (C) In|r*+ + 4x + + C 1 (D) + C x° +…

A: Proceed as shown below...

Q: d dx x= ||

A: Given that

Q: 5x 3x2 (3x²)' ework Diffeventiate the equntion. /3

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Q: S (2 +ల1) 2) dx

A: We have to find the value of indefinite integral

Q: P(A)=0.3, P(B)=0.6, A and B are indep, find P(AB'), P(A|B')

A: We have given that  P(A) = 0.3 P(B) = 0.6 If A and B are independent then, P(AB) = P(A and B) =…

Q: L {5-e²t +6t2} L {t²-3t 2e sin(3t)} MA L {t-t²-t+sin(√2t)} D

A: Laplace transformation formulas used are