D= fA)=2x + 24 X-16 D3= X=f"(D)= %3D

Q: V121–a² r85-x²-y² 11 x dz dy dx -157+x²+y²

A:

Q: Find 3 3x3 3 2Va ) dx - x5

A: here we have to find the integration of given function. the solution is following.

Q: 20x3 dx 2. JT2+1 Vx2+1

A: Explanation of the answer is as follows

Q: Find of y3 = x* + 3x d?y dx2

A: giveny3=x4+3xdiffrentiate with respect to x3y2y'=4x3+3y'=4x3+33y2

Q: 2. S (5x-12) dx x³-6x²+8x

A: Given, ∫5x-12x3-6x2+8xdx

Q: 1) f3x* dx +x dx 3) fxva² +I dx

A: We know that, ∫ xn dx = [( xn+1 )/( n+1 )] + C

Q: T (3 sec² x + 4 csc² x) dx 3

A: The given integral,        ∫π3π43sec2x+4csc2xdx

Q: •3 fx(2-x) 10. dy dx 0. r2VIn 3 VIn 3 35. •VIn 3 et dx dy

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

Q: dy :- 15x²y and y = 4 when x = -4 dx

A: To solve the initial value problem  dydx = -15 x2ydyy = -15x2 dx

Q: 18. V1+x dx 1-X

A:

Q: (x + у—4) dx — (х — у+2)dy %3D 0

A:

Q: Find 2 mnd dx² for y=( Snx)

A: Given: y=(sinx)x

Q: 4.2(х — у)dx + (3х — у — 1)dy 3 0

A: Let's find.

Q: [2 f(x)dx= 10 If then equals ?

A:

Q: X √2x²-4x-7 S dx

A: Solution…

Q: Sla 1 z dx |(25 – x²)3/2]

A:

Q: dx J-2 (5-4x-x²)/2

A:

Q: @3Dy+12 D3=24

A:

Q: Using basic rules of integration, find a. dr b. Jrdx c. fx'(-2r² - 8)dx 12x² – x d. xp- -dx 1-3х e.…

A:

Q: Evaluate the definite integral using the given values

A: Given: verify that ∫26x3dx=320 for verifying given integral we solve left hand side

Q: 7). Sx² sech x³ dx 3

A:

Q: f (x) dx 21 and g(x) dx 14, find 3f (x) + 5g(x)] dx.

A: ∫09f(x)dx = 21   ∫09g(x)dx = 14∫093f(x) + 5g(x)dx = ?

Q: 2. S (2x-5)dx x2-5x+3

A:

Q: S (Vx² + 1) dx 4 2

A:

Q: f(x)=10/17sqrt(6x^2+2x+6)= 10(6x^2+2x+6)^1/17, then df/dx =

A: f(x)=106x2+2x+6117

Q: (2x + Зу — 5)dx + (3x — у — 2)dy 3D0

A: Given the differential equation(2x+3y−5)dx+(3x−y−2)dy=0

Q: What is the value of ∫k3 f(x) dx given that ∫313 f(x) dx=−3 and ∫13k f(x) dx=4?

A: Given:The integrated values

Q: Find :a. b. 20 fő -1 20 dy (1+y) ² (20-6x) e 20x - 3x² dx

A:

Q: dx х V1-4 In2х

A:

Q: (3x4-43)dxc+(xy²-2x?4)dy:

A: 3xy2-y3dx+xy2-2x2ydy=0 fx,y=Mdx+Ndy ∂M∂y=∂N∂x For M=3xy2-y3∂M∂y=6xy-y2 For N=xy2-2x2y∂M∂y=y2-4xy…

Q: Q2: Find for y= (4x² +12)²(3x-20)² dx

A:

Q: 2. (D² + 3D + 2)y= 1+ 3x + x²

A:

Q: dy 4x2 + x dx y + 4

A: Given : dydx = 4x2+xy+4

Q: (#9) S x2 dx V16-x²

A:

Q: -.f x³ ex² dx 3

A:

Q: Find the antiderivative of dx/(49x2+16)2

A:

Q: 4 dx is equal to: xv16 - x2

A: we have to find the following integral

Q: Q3/ Solve dy dx4 2d²y + 1 = 0 dx²

A: Given d4ydx4-2d2ydx2+1=0To find solution:

Q: 9. S." §, x*V9-x dx 16 dx Vx-2 10.

A: We need to evaluate the given definite integrals, to sove we will use the substitution method.

Q: Sx³ In(x+4) dx

A: Solution is given below:

Q: 2Rx-3 + (x² – 3)] dx а. - (Rx2-3x+1)5

A:

Q: 5. St? V1- t dt (2x+3) dx 6. S (x2+3x-6)

A: Please see the answer below.

Q: d²y dy + 2 dx 12х — е2х || dx²

A:

Q: -2 S.f(x)dx -4 a. b.5°2f1x) dx C.5f(x) dx

A:

Q: dy у+x3 + 3x2 - 2х dx %3

A:

Q: Vx2-3 dx , x > V3, is equal to:

A:

Q: 5 dx is: V4-x2

A: Given:  Let I=∫54-x2 dx To Find: To evaluate the given integral.

Q: e6x (a) : dx 4+ e6x (b) /: dx 4+ e6x 3 (с) dx V4– x2

A: Since you have posted multiple questions i can answer first three as per our company guidelines…

Q: rlog 2 Vex – 1 dx -2 S, x8Vx2 – 1 dx x² x8 dx (a? Loc2)7

A: Sol