Evaluate xsec¬xdx using integration by parts. OA x2 -sec-1x-(x² – 1)3/2+c 2 O B. x? 1/2 2 Oc x2 -sec-1x-(x² – 1)3/2+c 2 O D. x2 -sec-lx -금(x2-1)3/2 + C 2

Q: The result of the integration sign(t-t)8(2t - 1)dr is 1 A. B.sign(t -) C. 5(2t+1) D. sign(t +

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Q: a) calculate and fully simplify ∫x^2cos(x)dx Hint: Considering a mnemonic for integration by parts…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Express the general solution in terms of Bessel functions: 4x²y" – 4xy/ + (16x² + 3)y = 0

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Q: Evaluate the integral. - 1 y° - 7y° dy У -1 9* У – 7y° dy = -Ty - 4

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Q: Tim The solution of the nonhomogeneous DE x'y" - 2xy' + 2y = 2x + 2 is y=c;x+c,x? + 2x?+x² - 2x'lnx…

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Q: The orthogonal trajectories of y = ce5z where c is arbitrary constant. is_ O z+ 2C = 5y O -2x + 2C =…

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: Evaluate the integral: Jxe dx хе -2x -xe -Xe 2x +C -Xe2x e -2х —хе +C 4 Xe 2: -2x хе -2x e +C -2x…

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Q: 15x²x³43x - 19 The integral f S can be rewritten as (x + 1)²(x² - 6x + 13) Ax + B C D Slax + + ax² +…

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Q: What is the general solution of the given higher order DE xy" + x(y')² – y' = 0 ? Select the correct…

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Q: Evaluate the integral. x dx (7x° + 3)* 5 (7x² + 3) * + c -4 O A. 56 7 O B. -(7x + 3) - +C Oc. -(7…

A: Given query is to find the value of the integral.

Q: 2+3x-7) X-2 dx Evaluate the integral: Se A²+ +In|3x-6|+C Ⓡ 1/²/₁ 2²+5x+! In/x-21 +C B 3 x²+5x+In…

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Q: 1 m ( x² + 3102=²7) dx x²+3x-7 X-2 Evaluate the integral: Se A +2²2 + — + In|3x-6√ + C Ⓡ X/²2 ₁ B…

A: A detailed solution is given below.

Q: The integral 2a12 + 5x° is equal to -dx 3 x5 + x3 +1 (a) -25 + C (2) +2² + 1)* (b) z10 +C (1 + کے +…

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Q: Evaluate the integral. 2+e-2x dx e3x 10 +C O -2e-5x(5e3x + 1) + C e Sx(10e2x + 3) + c 15 1 e 3* 2e2x…

A: The given integral is ∫2+e-2xe3xdx. Evaluate as follows.…

Q: By direct partial integration, Solve the following PDES 8- Xd²z 5 4 dz ду = 0, ₂ z(x,0) = x² +X, Z…

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Q: Find the integral. |(2x3 - 3x2 + x – 1) dx A x² + B 6x2 - 6x + 1 + C (c) None of the above x2 - x +…

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Q: The integraing factor of (4xy+3y² – x)dx + x(x+2y)dy3D0 is (A x-2 B 2x-2 2x-1 D D x2

A: Since, the given differential equation is not exact . To make it exact we find integrating factor ,…

Q: Evaluate the integral S dx 2x3 - 3xx 1 -In 2/2 "I/3x + /2 +C En(2 { x³ - 3x x)+c 1 V2 + V3x -In + C…

A: First we take common x3/4 then put√x=t  And using integration of 1/a2 - x2

Q: 3. (x³+xy²-y)dx + (y³+x²y+x)dy =0

A: We need to find the solution for (x3+xy2-y)dx+(y3+x2y+x)dy=0

Q: Evaluate the integral. J-Txe* dx -7(x +1)e -*+C a. O b. -7(x – 1)e*+C Oc. 7(x +1)e-*+C O d. 7xe-* +C…

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Q: 4 Evaluate the iterated integral (2x + y)2 d 3.

A: we have to find

Q: Reverse the order of integration in the following integral. 7 14-2x !! f(x.y) dy dx y14-2 Reverse…

A: From the given integral; I=∫07∫014-2xfx,ydydx Now find the x-intercept and y-intercept.…

Q: |1-y2 ху Q3. Evaluate the double integral dxdy /1– y²,

A: We have to find solutions

Q: Step by step

A: Given integral

Q: Recall the Power Rule for Integration for n + -1. un +1 + C u" . n + 1 In this case, u = 2x + 1, u'…

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Q: 5y + 5 5 dy 2y e - 5

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Q: 4 2 The reverse order of the integration o SEF (x, y)dydx is A) S S* f(x, y)dydx 0. 4 B) Só Sf(x,…

A: Here we have to change the order of integration.

Q: 3 By direct partial integration, Solve the following PDES 8- 82 Z 5 4 BB =0, Z(X₂0) = X²+X, Z (2,y)=…

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Q: Solve S using the technique of integration by partial x²-4 fractions A. In B. In +c с. in +c D. A В…

A: Option A

Q: 7. Evaluate the integral r8-2x (x + y + 1)-2 dydr.

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Q: 2 2х-4 2у — 1 dydx x + 1 ) Q2. Evaluate the double integral

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Q: 2. Find the integral 2x+3 dx x2-9 a. In/(x – 3)³(x + 3) + C а. b. In[(x – 3)³(x + 3)] +C c. 2ln[(x –…

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Q: State ALL the theorems on integration used in the following computation: 2 2 (32- 3 d - 23 3 3 -0) –…

A: Remark: The sum rule of integration is  ∫ ( f ( x ) + g ( x ) ) d x = ∫ f ( x ) d x + ∫ g ( x ) d x.…

Q: Evaluate the integral. 8+e-5x dx e6x 1 44 -5x +6 + C 30 O -8e-l1x(11e6x + 1) + C O .tel1x(88e5x + 6)…

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Q: 1. Use integration by parts to prove the reduction formula S(Inx)" dx = x(lnx)" – n S(Inx)"-1dx. %3D

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Q: Evaluate the integral. -2 4y2 - 5y – 12 5y - 12 dy У(у + 2)(у — 3)

A: Given that integration and we solve this integration by using general formulas of integration. Here…

Q: dx Evaluate the integral: (+3x-7) A ++ In|3x-6|+C 5 +5x+! In/x-21 +C B 3 с +5x+31n|x-2|+C D x² + 5x…

A: You must have idea about logarithmic properties to simplify this expression. Understanding of…

Q: The result of the integration sign(t-t)6(2r- 1)dr is 1 А. B. sign(t- C. 8(2t+1) D.sign(t +)

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Q: evaluate using Integration by Parts.

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Q: z+1 Calculate using residue integration method f. ;dz, c: |z – 1| = 1. z4-2z3

A: Given, ∮Cz+1z4-2z3dz,C:z-1=1 Here given the circle with radius 1 and center (1, 0).

Q: In x)2 To evaluate aX, apply integration by parts twice. For the second application of integration…

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Q: 7x Evaluate the integral -d.x. (x2 + 1)(2x – 2)

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Q: Find the integration inner product on C[–4, 2] of the given functions. f(x) = 15x g(x) = 2x³ %3D…

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Q: The general solution of 2y" -xy'+ (x - 24 ly = 0, is: OaC,xJ,) + C,xJ_(2) OcC,,(3) + C,xJ_(3x)…

A: The given equation is  x2y"-xy'+x2-24y=0                                  (1) The differential…

Q: The substitution z=y1 1 transforms the non-linear DE v + alx)v+ b(x)v2=D0 to the linear DE O z-…

A: The given equation is; y'+a(x)y+b(x)y2=0.

Q: – 30 - Evaluate the integral: -d.x x2 Vx2 + 16

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Q: x²+3x-7 X-2 +5x+31n|x-2|+C + +In|3x-6|+C 2 x²+5x+In/3x-6|+C x² + 5x + n/x-21 +C 2 3 In Evaluate the…

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Q: Use the substitution formula to evaluate the integral. 2/5 dt v/252 -1 -2/5

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Q: Evaluate the integral. 1 t3 dt t2 - 4 /2V2

A: ∫2241t3t2-4dt=?

Q: In ( x² + 3x -=-7) dx X-2 Evaluate the integral: Se Ⓒ + A x² 2 =+ + In|3x-6|+C ℗ +² +5x+3n|x-2/+C B…

A: To find out the integration.