For Exercises 5-7, simplify the expression. Do not rationalize the denominator. 2r(2r – 7)/2 – x( (2 7)-1/2 (2) - X (2x – (). 1 (2) V2x – 5. 2xV2x – 3 + x² 6. (2x - 7y (1)(r² – 9)'/2 7. (x² – 9) -1/2 (2x) - X

Q: 2xy+X=0

A: In the question it is asked to solve the differential equation given, dxdy-2xy+x=0.

Q: Evaluate (x² + 1)dA. Where D is shown below. y = -4 + x2 2-1 0 -2- 1 /2 3 X y = 4 – x2 2.

A: To evaluate the given double integral.

Q: x²-4y2 Simplify х2+4ху+4y2

A:

Q: 1 |(12x5 - 11)dx -1

A: ∫-1112x5-11 dx

Q: 9x2 + 8х — 7 lim 4x

A:

Q: -10(x-7)– 7(x+ 2)

A: i -10x-7-7x+2=-10x-10-7-7x-72=-10x+70-7x-14=-17x+56

Q: x+3/3-2x-12/9=1

A: The given equation is x + 3/3 – 2x –12/9 = 1.Assuming the equation is of the form,

Q: x dx Evaluate (4a² +9x?) 2

A:

Q: 2ln(x+3) = 3

A: Given equation is 2ln(x+3) = 3 To find : x =?

Q: y = -x - 5x + 6 and y = (x + 1)2 - 2 |

A:

Q: dx x²Vx? - 4) (x)

A: By substitution method, solve the integration. Put x = 2sec(theta)

Q: dx 9 + x2

A: Integrating the function of the standard form we have,

Q: 2x +3 x²-9 da

A:

Q: 1. dx x2 + 6x + 10

A:

Q: x4 – 5x³ + 6x² – 18 dx x3 – 3x2

A:

Q: 3x² - 8x + 1 | x² − 4x²+x+6 dx; use А x-2 + B x+1 + с x-3

A:

Q: -8x? + 16x + 8 dx (x – 1)2(x² + 1)

A: We will solve the problem

Q: óa b7 (a+b) (3ab) (3ab*)* Simplify the rational expression 3.

A: 6a4b7/(3ab)2×(a4b7)2/(3ab4)3 6a4b7/(9a2b2)×(a8b14)/(27a3b12)

Q: X Find | dx x²+8x+12

A:

Q: 7 x2 dx + 4x + 20 13

A:

Q: x2 + 8x + 15 = (x + 3)(x 4. x2 – 9x + 20 = (x – 5)(x.

A: Givenx2+8x+15we can rewrite 8x as sum of 3x and 5xx2+5x+3x+15taking common parts…

Q: √4x216x + 19 (x - 2)6 S - dx

A:

Q: 4 j (2²+V/F) 2√x dx

A:

Q: (5x – 2x2 + 6)8(x+2)dx

A:

Q: simplify 48. (x + 1)(2x² – x + 1) 50. (1 + 2x)(x² – 3x + 1)

A: Given :48. x+1 2x3-x+1To simplify the given expression .

Q: dx Evaluate f 4x- +4x+5

A: We have integral  I  = ∫dx4x2 + 4x + 5 Take 4 common from the denominator, we get I  = 14∫dxx2 + x +…

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

A: Solve the given equation

Q: 3x+ 3x+2- 6/22 C. 4.

A:

Q: d [(5 – 3x – 4x³)5(3x – 4)] dx

A: Derivative using product rule.

Q: d x メ

A: Given integration: ∫01dxx1-x It can be written as follows:…

Q: 3hx 3x 2. २ +२ ८

A: As per the guidelines I have to do a maximum of 1 question so I request you to submit the remaining…

Q: 4x- 4 H. x + 1 3x

A: We Know that, Tangent drawn from an external point to a circle are equal in length. Here, JF= 4x-4…