2 i) [x² ( x + ²7 - 2²/1) dx x i) Ï 0 x³ - 8 x-2 dx ii) ii) f (x³ + 3x² + 1) e-2x dx xe xe1+x dx

Q: X+1 dx (x- 1)(x² + x + 1)

A: The given integral is: I=∫x+1(x-1)(x2+x+1)dx

Q: (x-1) 12-3x dx

A: It can be solved directly

Q: x³-4x²-3x+1 1 - dx 3x + 2 5. f 6. dx

A:

Q: (x² (а3 — 2)da 4x +

A:

Q: 6+02+z*91taXtrực (x + 2)(x² + 3)² xp=

A: ∫3x4+4x3+16x2+20x+9x+2x2+32dx

Q: Vx - 2 dx 5 x*(Vĩ + 1)

A: I have stated the used formulas in the solution

Q: $x+ 2 4x -1

A: Given that                                                           I=∫8x+24x-1dx

Q: d/dx [(2x+1)3(3x2-1)4]

A:

Q: 9x +1 d) / | 3 – g² + 9x – 9) x2 + 9x – 9) -

A:

Q: 3. (1+4e3x)³ e3x dx

A:

Q: 2X + 2 ) dx 3. 2X 6 + 2e

A:

Q: 9x dx VI-9x -/1-9x2 +C -1 arcsin 3x + C + C 3(x3 – 3x)

A:

Q: 1-x dx (x- 3Xx-2)

A:

Q: dx V4 - x - dx 2 8)

A:

Q: 2. Integrate the following: /(x (x² + 7)*)dx a. 8x(x³ + 7)³(3x²) + c x³ ((x³ + 7)° + c 5 b. 3 (x³ +…

A: It is given that, ∫x2(x3+7)4dx   Here this integral can be solve by using substitution method.…

Q: Differentiate. y = In [(x + 4)(3x- 2)(5 – x)] d In (x+ 4)(3x – 2)(5- x))] = || dx

A: We have, It is known that the derivative of ln(ax) is, and derivative of the function of u.v form…

Q: X 4. f* - 2x² - 6x +1 2 x² - 2x-8 dx

A: We have to find the integral.

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

A: See the attachment

Q: 1 x2 - x + 12 x3 + 3x dx

A:

Q: 1) Find 1 x² +4x+13 dx.

A:

Q: (x²+1)dx 10. x2

A:

Q: (x² + 4)³/2 -dx

A: Given integral is: I=∫x2+432xdx Integrating it: Put:u=x2+4dudx=xx2+4dx=x2+4xdu…

Q: (cosh ar +h)dr

A:

Q: 8 11xe-x dx

A:

Q: 5x2+11x+2 dx x(x+1)²

A: integration using partial fraction

Q: 2 [(3x² + 1)(x³ + x)² dx [(3x + 8) ¹¹ dx 11

A:

Q: 1) 3 )dx

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

Q: dr Find if r (x) = 9x 2 + 5x – 3. dx

A: Given,            r(x) = 9x2 + 5x - 3

Q: x3+1 dx x3-x ii. dx iv. S: x(Inx)((Inx)?-3lnx+2)

A:

Q: -10 b) L,(x² + x)dx 10

A:

Q: Find O d² cot 1 ¹x dx2 -2x (1+x²)² 2x (1+x²)² -1 (1+x²)² -2 (1+x²)²

A: