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Q: Find the indefinite integral.

A: Given: I=∫5t+63dt  ……1

Q: Calculate the energy coefficient from the first order if the infinite potential box is as uneasy as…

A: Given: φn=2LsinnπxLφ2=2∂Lsin2πx2L To find: Solution

Q: E. Prove the following: 四- Iz.l 1.

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Q: b 1+ e2x Evaluate the integral. ex xp 1 + e2x

A: Given that: ∫01ex1+e2xdx

Q: 1. S ef = c f

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Q: Use substitutions to waite (In t)at, for seyo (1n ms of と in 0,9 € N, aE IR E IN, a E IR, a#0 where

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Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

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Q: d If g(x)=- -S*[e' - In (21+1)]dt, find g(x) Se dx 4 A (2x+1)² 4 B e+ (2x + 1)² Ⓒe* -In (2x+1) 2 D…

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Q: tes, sno W inut E [XY] = E[X] E[Y] E [g1(X) g2(X)] = E [g1 (X)] E [g2 (X)1 and

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Q: Q6) Compute the integral 3 1 dxp -з (х +2)3

A: Here we solve the given integral.

Q: If f(x, y) = e®¤ . In(16y), then fræ is given by: O 144 e9 In(16y) O - 81 e9 ln(16y) O 81 e9 In(16y)…

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Q: Find the indefinite integral. 3 8 dt = t3 t2 +C

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Q: For a non-negative integer n20, J,=| (In.x)" dx. Express J, in terms of J„- for n21. Hence, find J,.

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Q: Q16: Compute the following indefinite integral xʻe*dx

A: Please find the solution of questions.

Q: Q2 ) Evaluate the integral S*9/x7 + y²) dxdy.

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Q: Find the indefinite integral. | 15 7 19 – 14 d t8 - dt

A: We have to solve the integral

Q: Find the indefinite integral. t2 dt 3= t3 +C

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Q: .3 Q6) Compute the integral 1 -dp- -3 (x+2)3 12 a) 25 b) 0 c) divergent d) 50

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Q: Calculate the following integral: e 3x3 + 1 dw 1

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Q: 10. Find the integral| dt. t* +81

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Q: Show dz 4 In= 는I미페 - for a<0. x <

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Q: Sor's Evaluate e" 2e* 5e dx

A: The given integral is ∫ex2ex5ex dx

Q: Find the indefinite integral.

A: we have to evaluate the value of the given indefinite integral: ∫t2-3-t3+9t+1dt let the given…

Q: S 1.Prove that L (coswt): %| s2 +w2

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Q: Find the G.S. about xo = 0 for the following DE's (x²+4)y" + 2xy' - 12y = 0 1.

A: Please see the below pictures for detailed solution.

Q: Evaluate the integral. .2 5) t + dx t 1

A: Given,   ∫12t+1t2dx

Q: Evaluate the integral. 8t 8 e S dt 1+ e 8t 8e 1+e 8t 8t dt =

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Q: O Fined s where c is :-12-11=4 the ly Porbolic 7-2/4/2121

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Q: Find the G.S. about xo = 0 for the following DE's 1. (x² + 4)y" + 2xy' – 12y = 0 ||

A: Given DE is  (x2+4)y"+2xy'-12y=0 Given point x0=0 is an ordinary point.

Q: Evaluate Sm e" dæ. • 2 does not exist (diverges)

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Q: of J76-0 do 9 ☺ Sal loe doc

A: To find Integral

Q: (1+ 1)? dt =D t3

A: Given : ∫1+t2t3dt

Q: (a) / (e-t-2VE+1)dt

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Q: 4. Let V(t) be the amount of air in a balloon at any time t, find out whether the balloon is being…

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Q: d tanh¬' (In t) = dt 1(1 – (In t)²)

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Q: t DR) dende Dartine dövßes e te than show that Deo) X DR1) to DG20). o is atoxphic

A: To show D20×D21 is isomorphic to D420: Define a map f:D20×D21→D420 by fa,b=a×b a×b∈D420: Suppose a…

Q: e 2x Evaluate the integral of e* +1 xp-

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Q: *find te general Souliton hor the XZP +YZq =XM

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Q: ** If g(x) = S [e* - In(2t + 1)]at , find g"(x) dx ex. (2x + 1)2 A ex – In(2x + 1) 4 ex + (2x + 1)2…

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Q: Find the G.S. about xo = 0 for the following DE's 2. (1 + x²)y" + 10xy' + 20y = 0

A: answer is in next step. please give a like !!

Q: Find Hence evaluate d dr 1 Š S ₁ (1 +2²2)³/26 0 -1 1+x², dx.

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Q: Find the integral of t/(t^4+2) dt

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Q: 3t e"dt 2 (1+4e3

A: Let's integrate.

Q: H. If g(z) e2*z In , compute g'(r). What techniques should you be using in this %3! case?

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Q: Use the three-point Gauss-Legendre formula to evaluate the integral dx Ső (2x + 1)²

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Q: Evaluate the integral. 7e 7t dt 7t 3+ e'

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Q: e obtained by r

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Q: n²(ln(ar)) dr,a>0 J 2r In(ax) a.

A: