3(x5 + x³) ez"+xª + 3(x6 +xª) +2 dx -2

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: 17x-6 - dx x² -x² - 6x 2.

A:

Q: 1 X-X -dx ах 3, -8 2vx

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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

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Q: 6. (4x-6y- 1) dx + (3y – 2x – 2) dy = 0.

A:

Q: 7. Find. V2x dx - 1

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Q: Find 3 3x3 3 2Va ) dx - x5

A: here we have to find the integration of given function. the solution is following.

Q: 1. Solve x² - 2x- 2 d²y dx 2 dy 4y = x² + 2logx.

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Q: f(x)dx = 2, 5 and 8 f(x)dx = -5, then, 8 f(x)dx = -3

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Q: x3-27 dx 2. ズ-3

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Q: (3x -x2 dx 3.

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

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

A:

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

A:

Q: 2 sec2( sec-1x)dx xVx² -1 3. 3.

A: Here  we evaluate    ∫32 sec2sec-1xxx2-1  dx

Q: 4-y2 dx

A:

Q: 1) Evalvate - 5 dx ZV5 arctan x - 5 5 2 /5 arctan X-5 +C 2 x* - 5 arctan 5 arctan 25

A:

Q: -7, 2x (x2 + 1)dx

A: We can find the integration as below

Q: 5 ,2 X |x² + x – 6| dx -5

A:

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

A:

Q: -3 -dx J2 (x²–1)² 3.

A: The given integral,        ∫23xx2-12dx

Q: 1. (2x6x5 +7x³-3x² - 11) dx 2. f(9y2 +6y-4-y-5+1) dy (12x-x+x) dx 3.

A:

Q: 3. fx²(9-x³)5 dx 4. J√4x-1 dx

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: x4 – 4x3 + 8x² – 13x + 13 dx - - (x – 1)(x2 + 4)

A:

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

A: This question is based on indefinite integral.

Q: 8. f sec² (3x - 1) dx

A:

Q: 3-4x-10 x²-x-6 dx.

A: Given integral ∫x3-4x-10x2-x-6dx. The objective is to evaluate the integral.

Q: 2- Show that: -1 xb-1 In x dx b2

A: See the attachment

Q: 3r² + 10x + 7) In (z²+3) dz

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

Q: 1- S dx -4 4

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

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Q: 3 9 dx dt -1 -3 [:] 2 with a (0) = 4

A:

Q: 3 What is the value of -8e -2x+1 dx?

A: Consider the given integral

Q: 3- f xvx2 +1 dx

A: Integration

Q: x-4- dx x²-5x+6

A: Given, ∫x-4x2-5x+6dx   We have to integrate.

Q: 1-3x dx Jo J2x-3x² 4. 2х— Зх?

A: Given problem is

Q: 3)으 rcose de Jsine 1-x2 d ¿= xp 2

A: LEIBNIZ RULE

Q: (3z² + 1) dx (2 + 2x + 1)²

A:

Q: 3 = 4- 2y + - dx

A: The differential equation is,   The figure below represents the vector field of the differential…

Q: 5. j(4x²-5x+4)*(8x-5)dx 6X dx x ²-5

A:

Q: 2Rx-3 + (x² – 3)] dx а. - (Rx2-3x+1)5

A:

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

A:

Q: 2x + 5 4. -dx x2 + 16

A: Given: Let I=∫2x+5x2+16 dx To Find: To evaluate the given integral.

Q: 6-6r dx x-3x -2 In|x3 – 3x| + C In|x3 - 3x| + C -1 +C 3(x³ – 3x)

A: The detailed solution is given below Thank you

Q: 10x-25 -dx x²–3x-4

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Q: 21 (b), dx -1 3e2x

A:

Q: 3 2 - VX dx x² – 4 1 2]

A: ∫12xx2-43dxLet u=x2-4.=∫-3012u3du=12·∫-301u3du=1232u23-30=12--123· 323·32=-3-123· 3234

Q: 2. 16-x dx 2.

A: