1dx. x In x

Q: 1. lo' exp(exp(x)) dx

A: As per Bartleby guidelines i can answer only one question, kindly upload rest question seprately…

Q: 1 2.if [(fT))=, find [ f(4t) S

A: Laplace transform of the function

Q: dx 3 Losx

A:

Q: 4 Cosx

A: Find complementary function and particular integral

Q: Find dy for each of the fo llowing (4) y In (tax? tbx +c )

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Q: 6. f Vesx + etx dx

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Q: (as (4) = Solve for x on To, ZC)

A: we have to solve the following

Q: Find dy. 8.

A:

Q: Find de if p = In. - 7 dp da

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Q: b) exsin2x dx

A: To evaluate the integral: ∫ex sin2x dx Solution: Let I=∫ex sin2x dx…

Q: Evaluate: S(4sin (x) – 3sec? (x)) dx

A: ∫ 4sinx-3sec2xdx=∫ 4sinxdx-∫ 3sec2xdx=-4cosx-3tanxAdd a constant to the solution=-4cosx-3tanx+C

Q: in 4X when x dx

A:

Q: If y(x) = In 5a4, find y'(x).

A:

Q: that d (inx) =\xl"-;TT SX. dx %3D

A: We will use the sign-function σ(x) to prove the given identity. Where :  σ(x) = -1 when x<0 &…

Q: x[1+ (In x) ] xp

A: This question is based on indefinite integral.

Q: If ve* dy dx a.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: x→0 cot3

A: we are given  limx->06x cot3x which is = limx→06x( cos3xsin3x) if we apply limit we will get…

Q: 1 x (In x)3

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Q: 5x dy. 10.) Evaluate

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Q: 2) √ x¹ (5-x²) dx

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Q: Find Y = Coth 1 (x)

A: Given that y=coth-1x find dydx

Q: e*Vex-1dx ex+3

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Q: Is (x? + у)ах — хӑу %0 exact?

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Q: Compute the following. -[/x5+17x3+39x²+13] dx

A: ddxx5+17x3+39x2+137=

Q: S S dydx

A: we need to evaluate integral of, ∫02∫03y3dydx

Q: Activity 2: Find my Inec 73x+4 < 492x+1 1.

A: 1.    73x+4&lt;492x+1

Q: h(x) da (In(x), d

A: ddxhxlnxuse u/v rule:-

Q: dx Evaluate 3x – 12 O 1 O + 00 8

A: To evaluate the integral.

Q: (In(x))? dx

A:

Q: In2 fin² coshx dx

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Q: a. 1 L₁cos .x³dx

A: As per the Bartleby guidelines I am answering only first question. Kindly upload again and clearly…

Q: ex Evaluates (+8xy) dydx

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Q: Find amd inf of up B- g m, neN{ CR

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Q: dx 6) Stanh-¹ (in √x) x (1 - in ² √ x

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Q: dx x (In² x – 6 In x + 10) -

A: The Answer is:      Result = arctan ( ln x - 3 ) + C

Q: x* In xdr

A: We are asked to evaluate to integral.

Q: Evaluate: * dx re+1 5.) X-

A: Find your answer below

Q: Evaluate S X 2 ex² D dx

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Q: In x xp- dx 3- 2x In?(3x)

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Q: Зх + 1 h(x) = In 5x 2

A: Solution of the problem as follows

Q: dx S x? + x -2

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Q: Calculate x in degrees. [22 8X +5° 3X + 8°

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Q: 1. 43y こ。 It ex

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Q: Evaluate sec? xdx \3/2 96. '(1–4 tan x

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Q: . Evaluate e* dr dy 5y

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Q: 2) S(Inx)²dx

A: Recall: Integration By Parts Formula:         ∫u.v dx = u∫v dx-∫dudx∫v dxdx;…

Q: Evaluate /x In(10 x)dx

A: Integrate by parts: ∫fg' = fg-∫f'g

Q: Evaluate the following x4 (5-x²) dx

A:

Q: Evaluate x In x dx.

A: According to Integration by parts∫udv = uv -∫vduand choose u in this order ILATEI → InverseL → LogA…