6 iven differentinl ....(1x) dx = 2x+y with (2*)

Q: 3. (a) Determine S 2xe3*dx by using integration by parts.

A:

Q: Evaluate the integral: e³+cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 2In3 + C (3e)3+ sinh2x B 2 + In3…

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Q: 6. Evaluate the integral ex e* +e-xdx

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Q: 2 S (x) + x³)dx = ? -1

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Q: find integral x3 3) S dx /1-x²

A: We have to find the indefinite integral

Q: 1 (In x+1)x dy dx

A: Given integral is evaluated as follows

Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx 3+ (3e)3 + cosh2x A + C 2+2ln3 (3e)3 + sinh2x…

A: The integration are

Q: 2. Show that P(1-x)° dx= x'(1-x) dx. %3D 0/

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Q: 2. The rate at which the total average of COVID cases is dx increasing at x = 10 tents and 1 tent…

A: The solution are next step

Q: I. Find dy/dx of the following: 1. y= In 2x 2. y (In x) 3. y= In(tan x)

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³y³)dy = 0

A: According to guidelines I have to provide answer only for  first qiestion...Thanks

Q: dy y(ln y – In x +1) dx 1 C = -In None of the choices Option 1 1 C = -In C = -In- -ln Ontion3 Ontion…

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Q: 1 Integrate | tanhx dx

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Q: 5. Find the integral 1 -dx x -5x +6

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Q: In x /1+ (In x)² 6 S -dx

A: Given query is to eveluate the integral.

Q: OFind dy 9= (x²45x)"(x + Sec

A: The given function is: y=x2+5x4x+sec x5

Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 2+In3 +C (3e)3+cosh2x B) 2+2ln3…

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Q: IPydx dy 20.

A: To evaluate: ∫02∫13 x3y dxdy

Q: 1. Evaluate 5 S Sx (x + 3x)dydx

A: Given, ∫05∫0x x(x + 3x) dy dx=  ∫05∫0x (x2 + 3x2) dy dx=  ∫05 ∫0x (x2 + 3x2) dydx= ∫05 ∫0x 4x2 dydx

Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

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Q: 2 3. Evaluate the integral ||x dx -2 O 2 4

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Q: In 3 by Pots tien 3) S (4 - x)e"'dx calculate without integre (f Ju

A: Given,

Q: 3 a) Evaluate iNT=x² % dz dydx 1-x²-y² e-3(x²+y²+z²)ž

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

Q: 7 In x (1) Evaluate the definite integral dx.

A:

Q: 11 Show that dy dx = 1-In2. 8(xy +1) 0 0

A: Follow next step

Q: 18 2 6x dx using n = 2, 4, and 8 subintervals 2

A:

Q: Find So S 4:xy dx dy.

A: Evaluate the integral.

Q: 4. Evaluate the improper integral. dx х2 — 1

A: Consider the given integral as Solving the integral

Q: 5) Inx Iny mz dx dy dz

A: Given: Let I=∫1e∫1e∫1eln x ln y ln z dxdydz To Find: To evaluate the given integration

Q: 5. Compute dx 1+Vx

A: Introduction: Integration may be a technique of connecting elements to create an entire. we discover…

Q: 3/ Find Value of integral ) dx 0 X+1

A: I am attaching image so that you understand each and every step.

Q: 6. Evaluate the integral e* dx ex + e-x

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Q: fil experini for dy txďn

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Q: 6. Evaluate the integral. x³e2x dx

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Q: 18. Show that Vxª + x and Vx* x→o by showing that they both grow at the same rate as x² as x' grow…

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Q: 16 Evaluate ſ," x²In 3x dx correct to three decimal places.

A: Given- ∫12x2ln3x To find- The value of the above integral. Concept Used- The above integral can be…

Q: ¹In(1+x) -dx X

A: According to guidelines we must answer only one of the multiple questions given. So, I answer only…

Q: 7. Integrate the following indefinite integrals. 3e5x dx 1-2e5x a.

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Q: Evaluate L S dx dy. O 1 2/3 1/2 O 2

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Q: 2. Evaluate dy/dx for y= x In x 1+inx

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Q: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 +C B (3e)3+cosh2x 2+2ln3…

A: This question can be solved using integration by substitution.

Q: 19. f(x. y) In(1 - x - y) %3D

A: As per our company guidelines we are supposed to answer only the first question that you have…

Q: ormulas to compute the following antiderivative. x-1 x² -dx.

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Q: 2 1. Evaluate the integral: dx 2 x2-x

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Q: Evaluate S 0 2-9.x² dx using the Gamma function.

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Q: 13. Evaluate the integral dx x – 1

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Q: 15. Evaluate the integral 10 ·dx (x – 1)(x² + 9)

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Q: 3. SIX f- - dx x in x√√(inx)2-9

A: