1. Find the following indefinite integrals: 1 du b. fcos uchu = а. 1 fa'du- d. . du - с. 1+u? f. f- 1 du V1-u | secu tan udu g. csc udu =,

Q: Evaluate the indefinite integral: dz +C IV 36z2-1

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Q: dz 2+2vz

A: The given integral,       ∫dz2+2z

Q: In evaluating / (2x – 3) Vx– 2 dr by substitution, if 4 =x - 2 then what will be the resulting…

A: Given : Indefinite integral ∫2x-3x-2 dx   To find : Resulting indefinite integral by substituting…

Q: (b) 'elz)x d: 1

A:

Q: @ evaluate the indefinite integral fxº ex* dx

A: Given problem:- ∫ x8 ex^9 dx

Q: Evaluate the integrals

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Q: 24 Use properties of integrals to evaluate S (2x – 1) dæ,if 3 11 24 S (2x – 1) dæ = 104, and f (2x –…

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Q: Evaluate the integral from -n/2 to +t/2 of x² sin x.

A: Given integral

Q: By-1 dy 2y+1

A: We have to solve given indefinite integral.

Q: Find the indefinite integral. | (0.9t² + 0.06t + 2) dt + C

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Q: 2ea dx (ет — 1)2 1

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Q: Evaluate the following definite integral ,-(s-2)t sin(3t) dt. 3 2 (8 – 2)2 + 9 (8 – 3)2 + 4 - - O 1.…

A: Properties of Laplace transform  Lf(t)=∫0∞e-stf(t)dt Leatsinbt=b(s-a)2+b2 Lsinat=as2+a2

Q: Evaluate the integral: S/2 sin(4t - u) du dt

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Q: 6. Evaluate the fallowing real integrals by residue theerem ? dX ニ ans : こ。(X+a?)2 493 • I- ans B 12…

A: Let's find.

Q: Evaluate the indefinite integral: ∫t−6/11 dt

A: The integral of xn is given by: ∫xndx=xn+1n+1+C   Using the above rule:…

Q: 3. Evaluate the integrals √tanh x sech² xdx

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Q: evaluate the indefinite integral.

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Q: 2x(x+, こメP

A: Solve

Q: fxVx+5 dx :

A:

Q: 1. Determine the following integrals: 1- 2 (a) dar- (b) |

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Q: Show using residues that   the integral from 0 to infinity of dx/(1+x^6) equals (2pi)/3

A: We have to show that ∫0∞dx1+x6=2π3 by using residue theorem. Now, ∫Cdz1+z6=∫−RRdx1+x6+∫γdz1+z6 Now,…

Q: In evaluating (2r+3)Vx+ 2 dx by substitution, if 4=x+2 then what will be the resulting indefinite…

A: This can be evaluated as follows:

Q: Evaluate the integral

A: The integral is given by,

Q: If 3 h(t)dt = 5 5 and .3 h(t)dt = 7.3 what does the following integral equal? h(t)dt =

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Q: Determine the following indefinite integral.

A: The given indefinite integral is: ∫1x2-2x52dx Now, use the exponent property 1xn=x-n . ∫x-2-2x-52dx…

Q: 10. | Vi(1? + 31 + 2) dt

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Q: Compute the indefinite integral 2. 4e2a + 6x 5) dx. - -

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Q: 2. Evaluate these indefinite integrals: dt (d) S; dt 2t2+5t+3

A: Given that a integration  and we solve it by using general property of integration. Here i attached…

Q: 2 Which of the following integrals is equal to (3x – 5) dx if u=3x – 7?

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Q: 6. Evaluate the fallowing real integrals by residue. theerem 3 -bm -am 응) Co3 mX ans : X Sin mx ans…

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Q: de 2/2 V5 9 18

A: Solution: Here let I=∫dxx29-x2 Substitute: x=3sinu u=sin-1x3 and dx=3cosudu Thus,…

Q: S dy V1+9y2 3.

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Q: S Sen? (Ln y) dy

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Q: Show detailed solution for the following integral: (Non-anonymous questionO) S tan'z sec³z dz 7

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Q: 3 (x²–4)ž 4. (x2–4)ž

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Q: Consider the indefinite integral dx: + 8)°

A: Given,  ∫ x5x6+86dx

Q: - Prove using integrals Proper tos : e even sin()fc) dx=0 -b 9- For even functions.

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Q: Evaluate the indefinite integral.

A: Consider the provided integral, ∫z21+z33dz Evaluate the indefinite integral.  Apply the substitution…

Q: Evaluate the integrals in 1 1. Vx(1 + x) sin x sec x dx

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Q: determine Ahe impraper integral dx (H+1)(x²+1)

A: ................(1) use the partial fraction  ................(2) ................(3) take x=-1…

Q: d) Prove the results of the integrals 3 dx = 2+ In (2)– 4 [In (5)– In (3)]. x² +3x +2

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Q: Obtain a "reduction" formula that expresses the integral cos" x dx in terms of an integral of a…

A: Integration by parts: If u is first function and v is second function then: ∫u(x) v(x) dx=u(x)∫v(x)…

Q: In x dx

A: Given: ∫lnxx2dx Integrate the given integral using the integration by parts formula.

Q: 3 aluate the indefinite integral by using the substitution u = x + x° to reduce integral to standard…

A: Please refer to the image below

Q: ∫y + 3/(3-2)^2/3 dy

A: ∫ y+33-223dySimplify: =∫ y+3dyApply the Sum Rule:  ∫fx±gxdx=∫fxdx±∫gxdx=∫ ydy+∫ 3dy=y22+3yAdd a…

Q: 2 Which of the following integrals is equal to (3x – 5) dx if u =3x – 7?

A: Given∫123x-5dx

Q: (8) 18. Evaluate the following indefinite integrals: (a) / (5e* +7z + 1le") dr dr

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Q: Find the following indefinite integrals. Please don't forget "+ C".) 1/2 1/2 -1/2 dx -1 dr 2. (in=)

A: Given,    I=∫ (x12+1)12.12x-12dx   To solve this integration,    Lets substitute,…

Q: 7 Evaluate the improper integral, if exists : dx (5 – x)3

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Q: Determine the following indefinite integral. S ex 400-e2x dx, x> In 20

A: Given, ∫ex400-e2xdx