Question 13 | (10x+x*- 2r3– 3x2-6x+5)dx is equivalent to The definite integral A 2 (x-3x2+5)dx | 2(10x-2x-6x) dr B 2(x-3x2-6x +5) dx D 0.

Q: ce / √5³² + 25 de -dx Integrate X3 + C

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Q: S 3 (x + 1)(x² + x) -dx

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Q: 04 * O O Evaluate -1+2x-2x^2 -1+2x+2x^2 -1-2x-2x^2 -1-2x+2x^2 d dx 1-x fe 1² dt).

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Q: > Evaluate the Antegral dx ax45x +2

A: Rewrite the given integrand as follows. 32x2+5x+2=32x+1x+2=22x+1-1x+2

Q: How would I solve this problem using the product rule?

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

A: It can be solved directly

Q: 2 x + 4 dx 3x°+4x- 4 X 3.

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

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Q: Show that In (x+ Vx? + 1) x2 x + Vx2 + 1 dx x + / 2v x² + 1 X + V x2 + v2 +1 + 1 Vx+ 1 x2 + 1

A: This is a derivative problem

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

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Q: 5 S(4x² – 12x +9) ²dx

A: We use here binomial expansion and then we  integration.

Q: 6) Evaluate 0.8 1 0 dx 4x² +4

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Q: x2+1 - dx x4-x²+1

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Q: Calculate (3+1 x3+x a) using partial fractions b) using the substitution w = x3 +x

A: a) Given : ∫3x2+1x3+xdx  By Partial fraction  First, factor the denominator, we get 3x2+1xx2+1 =…

Q: x²+2x - 1 dx 2x3 + 3x2 - 2x

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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: 20 x3 25+x² 2)골 2 dx

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Q: x´ + 2x x' - x + x - 1 -d- .3 2

A: Given integral is ∫x2+2xx3-x2+x-1dx

Q: d Show that In dx 1 (a) x+2 x* +3x +2 1 (b) Hence find the exact value of dx in simplest form. r*…

A: iii.a. Quotient rule of differentiation states that ddxfg=f'g-g'fg2 Chain rule of differentiation…

Q: Integrate

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Q: x2 - 10x - 5 dx J (x - 1)2(x² + 1)

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Q: 1. Show that | (4x - 6x + 1)dx = (4x3 - 6x + 1)dx + (4x3 – 6x + 1)dx

A: Given ∫154x3-6x+1dx=∫134x3-6x+1dx+∫354x3-6x+1dx

Q: • N/W [ (x³-3x) dx - 1

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Q: S 1 dx (2x - 3)²

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Q: (5) Evaluate 75 2x -dx. 5x8

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Q: 1 2 3x + + 2x + 5

A: Given,         ∫13x2+2x+5dx

Q: 2. Prove that d [(2x+1)³] (2x+1)³(4x-19) (x-3)² dx = Then, -5 (2x+1)(8x-38) 3(x-3)² dx.

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Q: бх2— 2х +5 dx? 2х + 1

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Q: Evaluate the following x4 + 4x³ + 7x² + 17x – 9 -dx | 1. x3 + 2x2 – 3.x

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