(iv) S х2 +3х-1 dx x3-1

Q: 2 Find 2(x² + 3x - 1) xp- b. (x+ IX2x - 1)ar – 1)' dx x(x + 1) + 2 – 2x – x² a

A: We Use partial Fraction to separate the denominator and then integrate with respect to x.

Q: 9. Integral (2x-5) dx x²5x+3

A:

Q: •2 1 -dx- J-3 (x + 7)(x² + 16)

A: Given integral is Apply partial fractions to break the denominator

Q: | 2(x - 1)(x5 - 6x + 9)-5 dx

A:

Q: /25 – x² (-2x) dx 11.

A: 11. According to question,Given integral,∫25-x2-2x dx

Q: 1) S dx 9-x2 dx 2) J2y-2 x2Vx2 -2 3) dx 2 V1-x2 |3D

A:

Q: Thank you :D

A:

Q: 3 how that S 5x(1 – x²)² dx = 1

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Q: -) S xe²*dx .2

A:

Q: 27. ·√ √(x + 2√1-x²) dx _28. [₂ (2+√9 − x²) dx -3

A:

Q: 6. S: Ja2+1)2 dx x³ex? dx (x²+1)2'

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: · 8 Find f(x) dx = 5 (5 f(x) – 6) dx 8, and

A: Given ∫211f(x)dx=5∫25f(x)dx=6∫811f(x)dx=4

Q: -33e* – 105 -dx e2x + 8ex + 15

A: Here we use partial fraction method to solve the integral.   We know ∫1x+adx=ln(x+a)+C ln(ex)=x…

Q: S 2dx x(3(Inx)"+1지lnz-15)호 2 +13/nx-15)

A:

Q: 4-y2 dx

A:

Q: 13. S: 5x dx x5-3

A:

Q: 13. dx/(x²-4)

A: Since you have posted multiple problems we will answer first problem for you. If you need any other…

Q: -2x +5 Evaluate 10-4x -2y dy dx 3x 25 3

A: The given integral is: ∫01∫3x-2x+5(10-4x-2y)dy dx

Q: 1 x-3 x2-3x-4 dx

A:

Q: 19-x² dx 2

A:

Q: 2 1. x(-x² + 1) dx 16 dx 4x2 2. 3. dx x3/7 -V4x dx 4. 5. . (-2x! – x295) dx

A: According to the guidelines issued by the company We are supposed to answer only first three…

Q: Evaluate the definite integral using the given values

A: Given: ∫26x3dx=320, ∫26x dx=16, ∫26dx=4 We have to evaluate ∫266x-18x3dx Solution:…

Q: 32x ) dx In|xl + C 3 %3D - |- 3x. 2 In 3

A: let the missing term is Y

Q: 2. S (2x-5)dx x2-5x+3

A:

Q: b) Integrate: 2x + 5 -dx 2x*(x+3)(x –1)

A:

Q: x7= - 3x + 18 JZ - 54 in (3+ 57) + c 3/2 2 dx = %3D 3 + VX 3

A:

Q: 2 S (x² – 4| – |æ – 1)) dæ - 4| – |x – 1|) dx -2

A: Definite integration

Q: x2 - 3x/5 + 1 dx 1/2 3r7/s

A:

Q: 5. Show that (x² + 1)e-* dx = -x²e-x – 2xe-x – 3e-x +C

A:

Q: 1- S dx -4 4

A:

Q: 23-4x-8 Integrate: 2E+4) dx 1)(r²+4)

A:

Q: Q3. Evaluate S 2x+1-5x-1 dx 10*

A: Given that ∫2x+1-5x-110x dx evaluate the integral

Q: 4 4 + x2 Find 3 x° + + 4/x ) dx - -

A: Given integral, ∫x3+4x+4x2+4xdx

Q: dx S- x4 - 1

A:

Q: 3- f xvx2 +1 dx

A: Integration

Q: 2 S. x*- 4x +4 dx (メ-2)(x4) |

A: Solution: Consider the given integral is: I = ∫x2-4x+4(x-2)(x2+4)dxI = ∫x-22(x-2)(x2+4)dxI =…

Q: 1. ſe-5*dx el/x2 2. x3 5e 4lnx dx ,3.

A: ∫emx dx = emxm + C , where 'C' is the constant of integration.

Q: 4. Evaluate -dx. V16 – x2 -

A: Given integral:

Q: 2 1 dx V4-x2 1 dx xInx ーX xe*dx 1 8. 8.

A:

Q: 13. S 5x dx x5-3

A: To integrate ∫5x4x5 - 3dx

Q: 9. S." §, x*V9-x dx 16 dx Vx-2 10.

A: We need to evaluate the given definite integrals, to sove we will use the substitution method.

Q: x² +x-2 -dx can be resolved into (x2-1)(2x-x²)

A:

Q: (3) S 4-x² dx

A:

Q: 2 - S tần² (3x)sec²(3x)dx

A:

Q: 5 S Ix² x- 6|dx -5

A: The given integral,            ∫-55x2-x-6dx

Q: Sx² cos (x3 + 3) Van (x3• 3) dx + 3) Vsin (x3+ 3) dx 1)

A:

Q: fo³x² 10 xx(In x + 1) dx

A: The given integral is  ∫0∞x-xln x+1 dx

Q: 2. 16-x dx 2.

A:

Q: (4 - x2)3/2 dx 3

A: Consider, I=423∫-22(4-x2)3/2dx I =4232∫02(4-x2)3/2 dx   since f(x) is even function that is…