e2x dx= 1+e* A A 2e2x - In(1+ e*) +c B 8 e2x - In(1 + e*) + c C) e2X + In(1+ e*) + c D D ex - In(1+ e*) + c

Q: W Airport E -0° X = X

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Q: 2x+ 11 3 3 1 dx - X +3 Consider Idx - evaluate dx = x2 + x- 6 X- 2 X-2 x+3 x+3 In +C (x- 2)3 X-2 In…

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Q: 3ר2 d²y' |1+ () = c2 dx2 second order second degree first order third degree second order third…

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Q: x^n dx=x^(n+1)/(n+1)+C is not possible when    a. n=0   b. n=1   c. n=-1   d. n=2

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Q: * 5.8x √4x²+5 dx 2(4x²+5)³/2 A. +C 3 O A. OB. O C. * 6. f 35x-1 A. 35x-1 In 3 O A B 5x-1 dx C + C…

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Q: *dx 2x- In Ixl+ C 1 x² - In Ixl+ C | 2x 4 In Ixl+ C x² – 4 In Ix| + C O A В E None of the Above

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Q: & 38. Evaluate: √x dx A. x4/3 + C 3 4 C. ³x5/3+C B. x³/4 + C D.x3/5 + C 39. Evaluate: fx(4x - 3)dx…

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Q: L(e-3t)= %3D 1 s2- 3 1 .bO s2+3 S-3 1 .dO s +3 1.

A: We can solve it by definition of Laplace method Consider Le-3t = ∫0∞e-ste-3tdt=∫0∞e-(s+3)tdt=…

Q: 1. Evaluate: e 3z I = dz (e² + e5z)2

A: given integral I=∫0∞e3zez+e5z2dz claim- evaluate the integral

Q: x² +2x +3 dx x' +3x² + 9x A In Ix³ + 3x² + 9xl + C ! In Ix3 + 3x2 + 9xl + C 4 3. D 2 In I x3 + 3x² +…

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Q: 15x²x³43x - 19 The integral (x + 1)²(x² - 6x + 13) Ax + B What is the value of dx ? ax²+bx+c 31 -…

A: Given integral ∫15x2-x3-43x-19(x+1)2(x2-6x+13)

Q: 10x – 2 - dx . (x + 1)(5x² – 2x + 1) 16. Evaluate 5x - A) hx +1|+ n|5x² – 2x + 1|– tan +C 5x- B) Inx…

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Q: _42. Evaluate: √(√√x - 2)dx 3 A. ++ C x 3 B. - + C x C. 3 +=+ C 2 D. -*²_³+C 2 x 12 Evaluato: ((2x…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 2 x³ dx -6 √x²-9 Evaluate O44√3 24√/3 34√5 34√3

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Q: 3 1-x²-y² e-3(x²+y²+z²)² dz dydx 1-х2 a) Evaluate e-3(x²+y²+z?)² dz dydx

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Q: x²+x+1 g(x) Ja 2x²+2+x³+x dx = [Af(x) – B In(g(x)]à + D Sº , and if A =,B < 0, then S dx = ... x+2…

A: We are given a rational function to integrate. First, check if the denominator is factorizable.…

Q: (x-4x² +7x–9 - dx x-3 A x3 * - 4x + 3 In Ix-3 I + C C x3 * + 4x + 3 In Ix-31 + C B x3 x? D x3 x? +…

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Q: x2 dx (x– 1)3 1 In|x-1|- X-1 + C 2(x– 1)? 2 In|x-1| 1 +C 2(x – 1)2 X-1 2 In|x-1|- X-1 1 O Inlx- +C…

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Q: -2x dx 7. Evaluate (1–x)' A. x' + 6x - In(1-x)" +, -(1-x)* +C C. x' +6x + In(1-x)' +, (1-x) +c 1-X…

A: See the details solution in below

Q: 2-x Evaluate: dx 4x2+4x-3 긍 Im4x2 + 4x-31 + |2х-1 +C C.긍 I미4x2 + 4x-31 +. |2x+1 +C In In 12x+3 16…

A: We will use some adjustment and partial fraction method to solve this.

Q: dx = [Aƒ (x) – B ln(g(x)]å + D fa +2₂ rb dx Sa 2x²+2+x³+x² A 2x+²+5In(x + 2) + C x² B 2x + 5 ln(x +…

A: Given ∫abx2+x+12x2+2+x3+xdx=Af(x)-Bln(g(x)ab+D∫abdxx+2 and if A=15,B&lt;0. The objective is to…

Q: Evaluate √x² + x + 2 dx x²-1 x+1 In: +C (x-1)² 0₁ (x-1)² In- + C x+1 O x + 1 (x-1)² (x-1)² x+1 X+…

A: Solution is here

Q: x+x-2 dx If S (x²–1)(2x-x²) dx can be resolved into A S+ Bƒ f(x)dx + D ƒ g(x)dx , then

A: Using partial fraction to solve the problem.

Q: а) Tin) 3D 4T(n-1) — 3Т(n-2) + (n + 6)3". Т(0) 3 0; T(1) 3D 1 b) T(n) =3 T(n/3) + 2n; c) T(n) =2…

A: (a)  Given that,  Tn=4Tn-1-3Tn-2+n+63n T0=0; T1=1 We substitute, n=2 Then we get,…

Q: Find: S x² √√x – 3 dx =? A. (x-3) - (x − 3) ²/7 = 2 − 3)² + 6(x − 3)² + c B. ² (x − 3) − § (x − 3) %…

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Q: السؤال 9 L(e-3t)= .a O s2 -3 .b O S - 3 1 .c O s2+3 .d O s +3 1. 1. 1.

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Q: e (2e – 1) dx (ear – 2)*(e³< + 1)+ ,3x A 2e3x – 1 В 2e 6x – e 3x © (e3 – 2)4 +(1 +x?) @ E ,6x – e 3x…

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Q: 20 (i) E(13)* k=0 (ii) fºx'e-2= dx (iii) [ e-(z-13)²/8 dr

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Q: 2x3+3x dx x*+3x2 C A 2 In I x4 + 3x² I+ C In I x4 + 3x² |+ C In Ix4 + 3x? I + C - In Ix* + 3x? | + C…

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Q: 3x e 1+e³x 13. What is the best substitution to make to evaluate S O u = 3x Ou = e³x Ou=1+e³x O u =…

A: A detailed solution is given below.

Q: 53х dx (53x + 1)2 A) 3 V5x + 1 + C B) – 3 V5x + 1 + C In5 3 C) 3ln5 (V5x + 1) + C D) V5x + 1 + C 3…

A: As per the guidelines when multiple question are posted in single pic  then we are supposed to solve…

Q: L(e 3t) = 1 .a O s²+3 1 b O s +3 1 S-3 .d O s2 – 3 1.

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Q: t u(t-2) L. 31 O e3-2s (s+3)² 1. 2 s+3 e-2s 1 2 (s+3)? s+3 లాఓ-5 (x+3) -6-2부 2. +. (s+3)2 +3 (6+3)2…

A: The solution is given as

Q: x3+1 valuate: S* dx x+2 . x3 + x2 + 4x + 7ln(x + 2) + C c.x3 – x² + 4x – 7ln(x +2) + C -. x3 -x² +…

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Q: 2x²+ 2x+1 x+1 Evaluate: e dx. 1 + C X +1 A) x² + x +1 x+1 n|x+ 1| + C B - + In|x+ 1| + C D x2 + In|x…

A: The given integral is; eln[(2x^2+2x+1)/(x+1)].

Q: 23. What is dx? 3 – e4r e2z + V3 In e2r + V3 In |e2x а. +C C. +C 2 e2x – V3 V3 /3. b. V3 +C V3 +C 2x…

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Q: 1 e2x – e-2x dx = e2x + e-2x Hint: Try substitution with u = e2x + e-2x

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Q: 故(x3+5) ex A al d Iny d in5x

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 7) -U(X-2)(x+3)" (5x-1)(7x+ 2) 3х+13 6) 57 In7x+2+c) (ans.: In 5x 2х -3 7)Sー (ans.: -Im,x-1+ Im,x-2-…

A: ∫1ax+b dx =1alnax+b+C Note :As per our guidelines , we can solve first question .Please repost…

Q: 1 √√√x+x Solve the integral: S ® h1+x+c A C Gin|5+x²³| +c (B) : C © Bhl1+xel c C) + C 5 5 D) -n|1+x'…

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Q: x-e -2r -dx x²+e-2« *2(x-e-2«) A x²+e-2r xp- – 2(x-e-2x) dx x2+e-2r B -2x 2+e =21 dx x²+e-2¢…

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Q: 10 f(x) dx is exactly 5 1 A 5 f(5x+5) dx 5ff(² -1 1 B f(2.5x+7.5)dx -1 1 Ⓒ5 (2.5x (C) (2.5x+7.5)f(x)…

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Q: elser (i) E[X] (ii) E [(X – 1)21 (iii) E [3X – 1]

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Q: dx S is equal to e3x O 1/3 e^(-3x) + c O -1/3 e^(3x) + c O -1/3 e^(-3x) + C O 1/3 e^(3x) + c

A: To find: ∫dx e3x

Q: Find (5x-x)e* dx O(x-5x)e*-(2x-5)e"+2e* O (5x-x)e*-(5-2x)e" +2e* O (5x-x)e"-(5-2x)e"-2e O…

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Q: Transforming S Ⓒ √ 2²-22²2 =2 A -dz 1+z² z²+z B -dz 1- © S с © S D N dx using miscellaneous…

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Q: 3s (s-2)2 3e2 (1 – 21) 3e-21 (1 + 2t) In (출) 3te-21 3e2" (1 + 2t) 3t e2 6te2

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Q: Evaluate the definite integral

A: Given,

Q: Sx² et* dx 1 e x (8x2 - 4x + 1) + C 16 (8x2 + 4x- 1) + C e4x 16 e4x 32 (8x2-4x + 1) + C e* (8x2 + 4x…

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Q: Show that So e-ax J₁ (bx) dx= 1 √(a³ + b³)³ (a > 0)

A: