8. S 2+e x dx e-x

Q: s(VE + E dx

A: We want to integrate the given function.

Q: integrate ((x-1)e^x)/(x) dx

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Q: メ 2 4. Sô 5 dx

A: We have to solve

Q: 17 5. S dx х2+ 13х +1

A: We can use the following standard integration result to evaluate the given integral:…

Q: S(e2x + 1) dx =

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Q: In(x²+x)-Inx-elnx dx In(e(x+1)

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Q: 4 5. S (x + 5) (3x – 1) dx

A: As given by the question There are given that the integration: ∫04x+53x-1dx To find the value of the…

Q: 1 5. S z dx x²(5+x)3

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Q: S(x + 3)e*+6x dx

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Q: Solve the differential equation in Exercises

A: 21). Given differential equation is 1xdydx=yex2+2yex2. To solve the differential equation. Solution:…

Q: 4. J 5 5. S 12 7 in 3x dx 6. S (10 x - 40) dx x 2 - 8 x + 15 8. S

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Q: S (28*_ 4 e²_ 1) 2) dx |

A:

Q: 5 6 7 | || ? +y² +²) dx dy e -5 0 0

A: Given: ∫-55∫06∫07x2+y2+z2dxdydz

Q: 6. Evaluate: cin 4 a) (4x – 3) dx c) S* 2e* dx b) L, x²(-2x³ – 3)* dx d) ƒ dx e) S,(x + 1)(x² + 2x +…

A: (6) (a)To evaluate ∫254x-3dx Solution:…

Q: 2. 7. S(x³ – 6x + 5)* (x² – 2)dx

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Q: S csch-x coth x dx

A:

Q: 4. [csch(x)] = -csch(x) coth (x) dx

A: we know thatdifferentiation of cosh(x) is sinh(x) and vice- versa

Q: 5.5 dy √y.evy 6. Š dx X+ e 7. fete d dx 8. fdx

A: Here we have to find the integral.

Q: 6 S(3csc°C+) - &e*)dt

A: Given integration is : ∫3 cosec2t-8et dt To find the value of integration

Q: S(e* + x° + e°) +, x° + e°) dx .

A:

Q: (4) S xe*dx xe* + e* + c ex — хе* + с Option Option 2 хе* — ех + с Option 3

A:

Q: Use geometry to evaluate the following integrals.

A: Given: fx=2,0≤x≤53,5<x≤10 we know that ∫010fxdx=∫052dx+∫5103dx…

Q: 19. (E x' 3) dx

A: #19 Differentiation w.r.t. x

Q: (4) (d) 2-7 dx 4x-2 x²-1 (4) (e) S 7x (4x²+5)3 dx

A:

Q: 4. S ( 12 x³ + 15 x - 20 ) dx 5. S 10 x2/5 dx 6. § 3 ³V x8 dx 7. S ( 8 + 2 dx x3 x4. 8. S ( 2x³ -…

A:

Q: 22 Evaluate S- dx. 3/2 +1

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Q: 9. 23/2 3√x+1 - S dx

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Q: S (1/(X(Im)*) dx X(Inx)

A: LetI=∫1xlnx2dxLet u=ln(x)differentiate 1xdx=duI=∫1xlnx2dx.I=∫1u2du.I=∫u-2duUse power…

Q: 2. S 8sin*x dx 3. S 8cos*x dx

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Q: 4 ! 17) 8x In x dx

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Q: dx (x²+1)(x²-4)² dx (x²+4x+4) (x²-4) dx x(x+1)(x²+5x+6) S S S

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Q: 8. Sy'dy = 9 S 4x dx =

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Q: 1. S 7e*dx 2. S(5e* 6*)dx 3. § 3(5*)dx

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

Q: 1 [In(3x)] S (* -5x+2)e*dx

A: solution is given below

Q: 3 S Inx dx 1

A:

Q: d (e¬× In x) dx e-x e-x ln x – e-x e-× In x + O Option 1 Option 2 e-x e-* + X In x e-x +

A:

Q: 3 Solve S (x dx.

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Q: 10. ((ex-2)2 e 2x + 4 S dx

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Q: 2 (6) Sí x(x² – 2)dx 1 2

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Q: dx Evaluate e x(Inx)3

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Q: » [3] S Te dx > Vex [4] S(x- s(x + !)° dx >

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Q: Evaluate* e/x dx. x3 1 1 еx 1 ex 1 еx + с + ex + c - Option 3 Option 2 1 ex 1 еx 1 еx + с + ex + с -…

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Q: 5 1 3 √x² – 9 S dx

A:

Q: Sメtex dx

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Q: 6. Jo ex-3 S dx = 1- e2 – 9 2- e+3 2- e2+3 4- e+2

A: 6. We need to evaluate the following definite integral ∫01e2x-9ex-3dx

Q: a. S(x² – 1)e*²-3x dx

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Q: 12. Evaluate dx. et +e-

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Q: 4. s= dx = In]x| – e* + C %3D - ? S 2+3*dx = 4 + C In 8 5. S(D- dx =: 32x Inlxl + C 6. 3x. 2 In 3 3

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Q: 8). S coth 2x csch 2x dx (Apply u-substitution method)

A: