15x² x3-43x - 19 - (x + 1)²(x² - 6x +13) Ax + B S ax²+bx+c The integral What is the value of dx can be rewritten as dx ? Ax + B C D + + dx ax² + bx+c (mx + n)t rx + s] SE

Q: (3x-1)2/x+1

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Q: X^2-y^2÷2x-2y

A:

Q: 5**+2x (2x3 +1)dx *(2x3+1)dx

A: Use the following formulas 1.∫ axln xdx=axln a+c2. ddxxn=nxn-1

Q: Show that 22x-1 Г(2x) - r(x) r

A:

Q: 4x= o +4 X+1'

A:

Q: 3x + 10 dx x² + 2x + 5

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Q: x² + 4x - 4

A:

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

A:

Q: Q3) An open-top box is to be made by cutting small congruent squares from the corners of a…

A: Let the side of the square that is cut be x inch. After cutting the squares from the corners and…

Q: X2 dx ex+3

A:

Q: (√3-3)/6 - (√3+3) /6 12 dx 2 1+ (2x + 1)²

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Q: d. [(2x +1) (5a - 4)) dx 10x - 3 O 20x - 4 O 10x - 4 20x-3-

A:

Q: 2x3 – 9x2 + 11 dx x2 – 4x + 1

A: We know, ∫dxx=lnx ∫xndx=xn+1n+1 for any real number n.

Q: 2x + 3 dx 4x2 – 4x + 5

A: The objective of the question is evaluate the indefinite integral.

Q: 9(a + b) = 9a+

A: Given, 9(a + b) = 9a+

Q: (В y (62 - (52²-2³)) dz [² (62 − (52² − 2³)) dz + S* ((52² − z³) − 6x) dz 15+ 10+ 5 10 1 2 3 The…

A: Given data

Q: 3x+5 / 3x-1 = 5x+3 / x+1

A: Solve the given equation

Q: 2x³+1 Evaluate / 7+x-6 dx

A:

Q: 2-2x(x+7)   expand and simplify

A: Solution

Q: 2x2 − 6x Convert to a(x-h)^2 +K

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Q: 1 dx 3x (3-9x)

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Q: 2. -8p(p -3 - 10p) 5. (6a - 3b)(-2a) 3. m'(m + 2n - 6) 6. -3x(2x - 3)

A: We multiply each follow 2nd step.

Q: a) [(5x4 + 3x² + 2x + 4)dx b) [(Vx² + 7x)dx

A:

Q: x² + ax - 2bx - 2ab – x - 2ax2 - 2bx2 dx x* + ax² – 2bx2 - 2abx

A:

Q: 5x2+11x+2 dx x(x+1)²

A: integration using partial fraction

Q: 2x² 17x + 6 - ہے رہ (x − 2)(x² + 4x + 8)

A:

Q: Express as a polynomial. (2u +3)(u - 4) ( 4u+u ) 2

A: Given: y=22u+3u-44u+u For expressing given expression as a polynomial, we simplify given expression…

Q: 2 15х? -13 dx - 14х За +2

A: We will apply long division to solve integral

Q: √4x²(x³-5)ª dx = Ox³(x¹² - 25x¹ +250x6 - 1250x³ +6250) + c 12 15 O 16(x³ - 5)4 + c ○(x³ - 5)5 + c…

A: To evaluate ∫4x2x3-54dx Formulae used d(xn)=nxn-1d(constant)=0∫xndx=xn+1n+1+c

Q: f(2x. (2x + 6)5 dx 0 (2x+6)6+ C 2 H|M 3 12 (2x + 6)6 + C (2x + 6)6 + C (2x + 6)6 + C

A: A detailed solution is given below.

Q: d 4х +11 15. In((x + 1)(2x + 9)) dx (x + 1)(2x + 9)

A: Given:ddxlnx+12x+9

Q: (24+2x-x2)1/2dx

A:

Q: f 12x -9x +2 dx 3.

A:

Q: IT 5tan(3x) dx 12

A: Given ∫π12π95tan(3x) dx