5. (x²-x)? 5.*- 5. - x2 – 2x + In|x|+C x3 2 6. S(6Vx – x-3)2 dx 6. 18x? + x3/2 8 1 + C 5x5

Q: z dz 2). S: 25+16z2

A: We can find the integration as below.

Q: dy will be dx In x+1 If y = then 2x3 - 3x' (2x- 3x) +1)- (In x+ 1)(6x? – 3) (2x – 3x)? A. (2x - 3x)…

A: To find the dy/dx of the given function

Q: dz f1-42-223)2 3 4[3-2(2+パ) a. In 3+ JE (z+1)/ J3-2(241=+C 3-4,(2+)? 3 b. 4[3-2(2+1=)] C-A(24)?…

A: Given ∫3z(1-4z-2z2)2dz ∫f'xfxdx=lnfx+c

Q: 6 4 for f(x, y) 3 3x у" - 4x"у. 5 3 Verify that дх ду ду дх of 4 5 3 4 18y x - 20y°x dx 18x°y -…

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Q: |(In 6x)2 dx ОА. x(In 6x)2 - x(In 6x) + x + C В. x(In 6x)2 + 2x(In 6x) - 2x + C с. x(In 6x)2 - 2х(In…

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Q: 4. 5 Show that if y%= x+4 then dx (x+4)** %3D %3D 16. dx. 2 (x+4)² **n Hence, find the value of|

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Q: Find L-1. by convolutions. l(s-1)².

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Q: 10. f(1) = –0.5 and f(n) = f(n – 1) – 0.5 for n>2 %3D - -

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Q: 4 (iv) F(s) = s2 +9 2s + 16 (v) F(s) : s2 + 4s + 20 3s – 15 (vi) F(s) %3D 2s2 – 4s + 10

A: The Laplace transform of a function is an integral that converts the real variable into complex…

Q: dy -is If y = In(x-5), then dx 4x x-5 4. 3x 4 x-5 4x 3. 4x +5

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Q: 14. Evaluate the integral: (x² + 3x)° dx A. (x* + 30)' + C 3 x* + 3x' + C C. +C (x² + 3x) + C В. D.

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Q: Evaluate In x dx x3 А. In x x3 1 In x 2x2 1 + C 4x2 В. In x dx 1 1 x3 In x - 2x2 4x2 + C С. In x dx…

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Q: (in) S 15:22 15-z dx. u = (M S 15 - TV9 – a² dx. u= (vi) S dr. u = 22+15

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Q: 3. y = In (3x – 7) %3D 9. 5. y= Inx? - 1) 7. y= In (1 – x²) 9. f(X)= In (4X 6 + 2X ³) -+ 1)

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Q: IF y = u+ + 3u2 & u = 2x 64x3 + 30x 8x(8x2 – 3) الخيار رقم 1 خيار 3 Find dy dx 8x(8x2 + 3) 8x(8x3 +…

A: We can find the derivative as below.

Q: _6. If we evaluate S x²(5+ 2x³)®(3x – 2)dx, and let u = 5+ 2x³, what is du? А. х2dx D. (5+ 2x³)dx В.…

A: As per the instruction, we are solving only one question. If you need an answer to others then…

Q: 5. Suppose that f (x) dx = = 5, f (x) dx = -3, g(x) dx = -1, and g(x) dx = 2. Compute | (2f(2) –…

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Q: 6) calculate In (2e°)= 11 2= 0.7n 3= 1. || ln5=1.6n7=20 %3D n(2e°)=X L ex =In 2

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Q: 11. (4+ t) dt 13. | – 5y) dy 15. (31² – 4t + 5) dt

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Q: 1. f'(x)dx if f(2) = 1 2. f(x) = S(x² + x – 3)dx if f (2) = 3 3. f(x) = S xe*dx if f(2) = 3 4. f(x)…

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Q: 9. Solve In (x+5) 2 2. O A. (x | x 2 12.3891} B. (x | x 2 2.3891} O C. (x |xs 12.3891} O D. {x |x s…

A: Given:         ln(x+5)≥2

Q: ++4 if X < 3 f(x) = { x2 + 1 if -3 sx<5 %3D x-7 if X25

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Q: -5x² +11x+2 x(x+1)² dx 2ln|x| +3 In|x +1| + + + C x+1 Option 1 2ln|x| +3 In|x +1| +++ C Option 3…

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Q: -10 9. If S"f(x) + g(x))dx = 10, Sio g(x)dx = 3 and So 3f (x)dx = -45, 10 find f(x)dx

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Q: x2-2 x+1 x2 --x-In Ix+11 + C C. + x- In Ix+ 11+C x2 -x + In Ix + 11 + C 2 +x + In Ix+ 11 + C O B

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Q: dx Vx3 1 -4 In|x/4|-4x3/4 + C -4 In|x/|- 4(1- x) +C Option 1 O Option 2 -4x4-4 In|1-x'/4|+C 4…

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Q: 1. Evaluate the integral [(4z° +3z2 +2z– 6) dz

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Q: -l<-<-1 10 A -10 В -10 10 10 10 -1 0 D -10 E -1 1 10 -T0 -1 10 F -10 -1 0 1 10 G -10 -1 1 10 O A Ов…

A: The given inequality is: -1&lt;x10≤1  To graph inequalities.

Q: 1 Find xIn(x15) dr. xln(x!5) 1 а. xIn(x!5) 1 -In] In(x!5) |+ C 15 1 dx = In] x'5 |+ C b. xln(x!5) 1…

A: Use the substitution method and integrate the given expression.

Q: If y = (5x+ 1)(2x- + In x), then will be dx A. (5x + 1) (+;)+5(2x-1+ In x) В. B. (5x + 1) (-) +…

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Q: ex-4e-x ex 2 x-² / + C ex Option 1 dx 2 x + ² + C ex O Option 3 x+2 ex + C O Option 2 x-2e * +C O…

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Q: dy If y = ( a² +1) (x³ + 3) dx %3D O 5x^4 + 3x^2+ 6x 6x^3 O 2x + 3x^2 O 2x^2 +2x+ 3x^5+9x^2…

A: Question 1,Given,            y=x2+1x3+3To find: dydx

Q: de xdx 1. (In* 4x-1) 2. V3x +5 sin 4x de de 4. 9+8cos 2x 3. (5x-3)dr 5. 3x-3x+2 (3-4x)dx 6. TAx…

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Q: 5s +1 To determine L-1. |s² – s – 12

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Q: _4. In evaluating: S(3x² – 4x + 2)*(3x – 2)dx, if u = 3x2 – 4x + 2, what is du? А. 6х —4 В. 6х dx C.…

A: As per guidelines we have to solve only three

Q: 46) Evaluate V(3r + 1)dx 2(3r+1)7 O s(3z+1) 2 O 2(3z+1)7 +c 3 O D(3r+1)1 + c 2

A: We have to solve the given integration

Q: 8. Compute using the trig. substitution S x2 -dx (1–x²)1/2

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Q: 9. S(9 + 8y – y²)= dy

A: Topic = Integration As per guidelines , At  a time only one question can be answered . please repost…

Q: If y=2x²-4, what is its inverse? or Oy¹--√2 Dy^--, DOIN such that xs-4 such that x2-4 such that x20…

A: Given, y=2x2-4 To find the inverse, we need to swap the variables 'x' &amp; 'y' x=2y2-4 Now solve…

Q: In x Compute -dx. 3√√/x 9 X 3 A²x²0 nx-x²²+ C A.- In 2/3 2 4 1 B.- - +C X 3 4/3 4 3 C.--(In x)x-4/3…

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Q: .7 f(x)dx= 12 and f(x)dx = 3.1, then 5. If %3D

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Q: dx = 2x - 1 x³+3x + C x2 +C -- 3+C 2. 6. In x +C In x +C

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Q: 1+ In x If y = 1- In x The value of y' = 10.62 at x = 2 %3D

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Q: x is within 5 units of 1. Olx-1 s5 |x - 1|> 5 |x -1|2 5 Olx-11-5

A: We will solve the problem

Q: L() tu(t-3) e6-3s ( 1 + (s+2} 3 s+2 e2-3« ( + ) o 1 (s+2} S+2 e-3+ ( +) o 1 (s+2} s+2 ( e-6-3s 1 3 +…

A: We will find out the required value.

Q: 2/3 If y = xl/3 + 2 dy then |z */0 =-8 dr

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Q: Find dy/dx: y = 10x (2a5+7) 2 a. 243z 243x 2(32 +5) 2 O b. 2(32+5) 2 450z 10 11 (2a5 +7) 2 (2x5 +7)…

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Q: 7. Evaluate the integral x4 6x5 1 dx

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Q: 4. V21+4:-z dz

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Q: 4 1** ƒ(z)dz = 3, and [*9(2) If f(x) dx 5 g(x) dx = 3, then an [*14ƒ(z) + 6g(z)]dz ==

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