30 en (6ox+ 3o)dx 2.

Q: (-1)^ dx n= (2n+1)!

A:

Q: 2 x 4 x Se core* csc*e* dx

A: ∫ex cot2ex csc4ex dx=∫ex cot2ex csc2ex csc2ex dx=∫ex cot2ex 1+cot2ex csc2ex dx      ∵csc2x-cot2x=1…

Q: -3* dx. Evaluate O2 3 3 +1

A:

Q: 2 (x-4) dx = (S %3D 2.

A: Given : The definite integral is ∫02 ( x - 4 )2 dx .

Q: ,2 3 csc- x dx 1. /1–4cot2.

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the next…

Q: 13. (x² + y²)dy dx

A: The given double integral is,

Q: - (64 – 2²) " - dy dx %3D

A: Solve the initial-value problem for y as a function of x.     64-x2dydx=1 , y0=6

Q: S S, 4cosx² dx dy

A:

Q: -33e* – 105 -dx e2x + 8ex + 15

A: Here we use partial fraction method to solve the integral.   We know ∫1x+adx=ln(x+a)+C ln(ex)=x…

Q: 2. S (4x³ + 2x²) cos(2x) dx

A:

Q: 13) Find / VI- 2x dx by the method of substitution.

A: Substitute   1-2x = t

Q: 2x – 1 - -dx x2 – 6x + 18 6x + 18 (구) -ㅇ 2 In Va? – 6x + 18 + 2 In +arctan 3 3 3 O A O B

A:

Q: .3 9. dx dy y2

A: Find the double integration.

Q: 12. S e 3In(2x-1) 2x - 1 - dx

A: The given integral is: I=∫e3ln2x-12x-1dx   As we know the Power Rule: ∫ax+bndx=ax+bn+1an+1+C

Q: d Find dx (46z + 3) -

A: Answer  We know that ddx(af(x))=af(x)ln(a).f1(x)

Q: 3x -1 dx is equal to

A:

Q: 7. Se* (1 + 2e*)* dx

A:

Q: 9/ (4x’y² - 2xy)dx + (3xʻy* - x*)dy = o

A:

Q: 49 x6 dx Integrate: 24 + C

A:

Q: 6ху — Зу? + 2y) dx + 2(х — у) dy %3D 0

A: This is a differential equation. and here we use integration and differential methods .

Q: 1 (a) dx + 25x2 4 -

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: 1 7) So dx V36- x2

A: Solution of the problem as follows

Q: 13 – 2r dx 1.

A:

Q: 2) (-4у + e-3*)dx %3D 4 dy

A:

Q: 4. (x³ + 3x – 1) dx 2 5. 4x x2 6. SIy + 1) – (y? - 1)]dy

A:

Q: 6. J 4 x4-1 -dx

A:

Q: 5) (2xy -3y) dx + (x-x) dy = o

A:

Q: • 4 13х + 12 -dx x2 + 3x 3

A: ∫3413x+12x2+3x-4dxApplying completion of squares:=∫3413x+12x+322-254dxSubs u =…

Q: 2x Eyaluate dx . 1-4x4

A:

Q: (2x+5)dxt 3y dy = o

A:

Q: 5x4 dx x5-3 S4 cos (-3x + 2) dx [ 4cot 5x csc25x dx

A: You can solve these integral problems by using the method of substitution.

Q: ( 2x-sy+12) dx +(7x-4y+15)dy = o 2,

A:

Q: 5 (a) | x² In(2x) dx (b) x'e*dx 'xp, Jo

A:

Q: 5- (2xe" + e')dx + (x² + 1)e³dy = 0

A: solving given DE by separation of variables.

Q: 1. ſe-5*dx el/x2 2. x3 5e 4lnx dx ,3.

A: ∫emx dx = emxm + C , where 'C' is the constant of integration.

Q: 2 1) (-2xy) dx + ( Sing-x²) dy

A: As per our company guidelines we are supposed to answer only the first question. Kindly re post the…

Q: 3 I= |(e* +x² + A\dx Дх 3D0, 25 1

A: Solve the following

Q: (5) (2х — у) — 2у — х dy dx

A: As per the guidelines, we are supposed to solve only one questions as multiples questions have been…

Q: 3. (х+1)dy %3D (2хe* - ху- 2у)dx

A:

Q: 1 dx 7х — 2 1 In(7a — 2) + с 7 -

A:

Q: 3 .4 ²³₁₂₁ (4x²y — z³) dz dy dx

A:

Q: -2 3. Integrate: [8x°e"-2 dx = du - e* 4x°dx 2 du = dex?. 4x° dx 4 3 2ou 8 ex".x°dx

A:

Q: 1. (2y³ + 4) dx = (6-2xy²) dy

A: As per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: 3 V3x x2 dy dx O 27 O 54

A:

Q: 3 Evaluate: 2₁ (4x²yz - 2 ) dz dy dx 4

A:

Q: 2 8 (x² – 2y2) dx dy

A: We need to integrate∫12∫08x2-2y2dxdy

Q: iv) L,x²e=* dx -2 -3x dx 1

A:

Q: 21 (b), dx -1 3e2x

A:

Q: С (4 — х — 2у) dx dy

A:

Q: 16 13 cosh (Vx) dx 1

A: To evaluate the given definite integral.