d²y dx² 2 (2x-3)² Find y = O O d²y dx² d²y dx² d²y dx² O d'y dx² = = = = 12 (2x-3)¹ -12 (2x-3)4 48 (2x-3)* -8 (2x-3)³

Q: 2x dx e2* +3e" +2 5.

A: To solve this integral, a substitution of is taken. Then it is differentiated to find the value of…

Q: d^2y/dx^2-6dy/dx+9y=3xe^-3x+3x^2-2

A:

Q: 2x+x-21x+24 dx x² +2x-8

A:

Q: 2x dx (x*-16)

A:

Q: * бу dx 2 =x+y

A:

Q: e* (x + 2) (x+3)² dx

A: To evaluate the following integral.∫exx+2x+32 dx

Q: 3dy dx3 +5ª²y _ 2 dy = 0 dx2 dx

A: Follow next step

Q: dy If y = (5x + 1)(2x +In x), then will be %3D dx (5x + 1) +) + 5(2x+ In x) A. -1 B. (5x+ 1) - 2. +…

A: The given problem is to find the derivative of given function y=(5x+1)(2x-1+ln(x)) , we can use…

Q: b. S 2*³-4x²-x-3 dx х2-2х-3

A: First we divide the polynomial  using long division

Q: | 4.0°e-9* 4x³e-9a* dx

A:

Q: 7. ₁²5(5x - 3)² dx

A: Here we have to find the definite integral.

Q: 4x² + 5 -dx 3

A: Given, integral is

Q: If y 3 , then dx 5x2-3 10r2 3V/5x2-34 35x2- 3) 5x2-3 10x 3 3(5x2-3)2 10r 3 35x2-3)

A: Find the derivative of the given function.

Q: NIFN dx √2x (√2x + 9)

A: Given query is to find the value of the integral.

Q: -| Vx³ + 16x² dx

A: Let I=∫x3+16x2 dx I=∫xx+16 dx Let assume x+16=t2⇒dx=2t dt I=∫(t2-16)t(2t) dt =2∫(t4-16t2)dt

Q: (x^3 + x^4)dx + 8y^(3)xdy = 0

A: x3 + x4dx + 8y3xdy = 0

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

A:

Q: (12x-4)dx (3x+1)³(2x-2) 3

A: We have to find out the integration.

Q: Find / (+52 + 4) dz 5x x6

A: Given integral: We have to evaluate the given integral.

Q: ① -2) (7x 0 - 3x - 2 + 이승 이승 ② 1 ( + ex) 2 dx Hx2

A: (1)ddx(7x6+3x4−2x)

Q: 2x+6)dx x²+2x+5

A:

Q: EVALUATE THE FOLLOWING: 1. S(5x5-6x + 2x +55)dx (5x-4x*+7x)dx 3. SV5X+7 dx

A: (1).                                ∫5x6 -6x4 + 2x+ 6dx…

Q: • N/W [ (x³-3x) dx - 1

A:

Q: x + 5X" + 4X - 3 dx (x² + 3x + 5) (x²+7X+12)

A: The given integral is ∫x6+5x4+4x-3x2+3x+5x2+7x+12dx.

Q: (2xey + e)dx+ (x² + 1)e'dy = 0

A: We want to solve the given differential equation. To solved the differential equation, initially we…

Q: (x3-4) 2. S dx x3+2x2+2x

A: To evalaute: I=∫x3-4x3+2x2+2xdx=∫1-2x2+2x+4x3+2x2+2xdx=∫dx-∫2x2+2x+4x3+2x2+2xdx

Q: 9) (4y? + 10xy – 4y + 8)dx + (2x² + 2xy – x)dy = 0 ; when y(0) = 1 %3D

A:

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.

A:

Q: sCx²-(4x+d)" (2x-4)dx

A:

Q: Determine an expression for expression for 3(y-2)³ − x² = 4x − 6. dx

A: Solving the problem by finding the value of the problem by finding the value of the derivative.

Q: x4

A: