21. 1dx dy -3

Q: 4 ( Calculate -2x dy

A:

Q: 2)S 1xtil dx (5)

A:

Q: メ 2 4. Sô 5 dx

A: We have to solve

Q: 17 5. S dx х2+ 13х +1

A: We can use the following standard integration result to evaluate the given integral:…

Q: 21. In 3x dx

A: Given integral is

Q: 4. S sinºx dx

A: This question can be solved by applying the concepts of integration of trigonometric functions.

Q: 3. 1- xZ dx

A: The integration of the integral is x4sqrt(1-x2), limit from 0 to 1.

Q: 12 (4x – 5y) dy dx

A:

Q: Evaluate the integrals

A: Given, ∫ln 6ln 7∫0ln 2∫ln 4ln 5 ex+y+z dz dy dx

Q: Solve the initial value problem.

A: The initial value problem: dydt=2t+9t2, y1=2

Q: 5. S(-5x-6 + 10x-11 – 20x-21)(x-5 –x-10 + x-20)dx

A:

Q: 10 ExiafxIn(3x).dx.

A: Use integration by parts.

Q: S tanh 2x In (cosh 2x) dx

A: Given integral is, ∫tanh 2x lncosh 2xdx

Q: х In 3x dx

A: Given:

Q: (In /3)/3 24) З е3x dx 1+ ебх

A:

Q: 25y2-4 dy 415 S. 2/5

A: ∫254525y2-4y dy Put, y=25secθ Differentiating with respect to θ, we get ⇒dydθ=25secθ tanθ⇒dy=25secθ…

Q: In (ax-1)dx

A:

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: Integrate S (2x+1) Staz+X+4) dx

A:

Q: 13x +5 If x- 2x dx = A In|x

A: Given that, ∫13x+5x2-2xdx=Alnx+Blnx-2+C We have to find the value of A + B.

Q: In(3x – 2) dx

A: It is known that: ∫ln xdx=xln x-x+C, where C is the integration constant.

Q: ,3 In x dx

A: Solution

Q: Expand d/dx (Yx)

A:

Q: (4) S xe*dx xe* + e* + c ex — хе* + с Option Option 2 хе* — ех + с Option 3

A:

Q: In(13x) Integrate: S dx x7

A:

Q: (2х+1)2 dy 4. У - 1-2х dx 12/09/2021 10: 00

A: We have to solve the problem

Q: 2 Evaluate S S dx dy dz.

A: Evaluating the definite integral

Q: L{t – e-3t} = + s-3 L{t – e-3t} = =-- I. II. s-3 L{t – e-3t} = +3 L{t – e-3t} = III. IV. %3D s+3

A: We know the Laplace transforms Ltn=n!sn+1, s>0 L ea t =1s-a, s>a Now, Lt-e-3t=Lt-Le-3t L t…

Q: 2 What is wrong with the equation dx =

A: Use the formula ∫xndx=xn+1n+1, to evaluate the indefinite integral ∫4x3dx.…

Q: 1 [In(3x)] S (* -5x+2)e*dx

A: solution is given below

Q: . Evaluate S (-+ 3e* ) dx

A: We have to Evaluate  ∫ {(1/√x) - (2/x) + 3ex} dx = ∫(1/√x) dx - 2 ∫(1/x) dx + 3 ∫ex dx

Q: •4 (ii) 2y dy dx.

A:

Q: 2 S dz = 3. S dv

A:

Q: 0- 19el+2x° dx 22.

A:

Q: 1 3. Evaluate dx, using substitution method. 2

A: The given integral is: ∫1xx+12dx I=∫1xx+12dx    -1

Q: exey (2xe + )dx + ( ) dy - ex ر ول

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: + 4 oly +6y =0 dt dy +2 -6x=6

A: Introduction:Simultaneous equations are those in which the derivatives of two or more dependent…

Q: 27. Find S." ( + 2x + 6) dx

A:

Q: 3 .4 ²³₁₂₁ (4x²y — z³) dz dy dx

A:

Q: 15. If y3 – xy = 5 ,1 d²y then dx2

A: y3-xy=5

Q: Find dy/dx of 10x - 18xy2+10y3 = 48 9y-20x 3 (бу? -5ху) dy !! dx 9y-20x dy 3 (буз - 5ху) %3D dx dy…

A: topic - implicit differentiation

Q: Sメtex dx

A:

Q: Inx dx

A: Substitute Ln(x) = t and use integration by parts.

Q: 4 3x+2 dy %3D 2x-1 dx 12/09/2021 10: 00

A:

Q: . In(3x) dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 10 Find ſ," (+ 2x + 6) dx 4 x6

A:

Q: In (Inx) dx

A:

Q: 16 13 cosh (Vx) dx 1

A: To evaluate the given definite integral.

Q: 9, (x2 + 2x - 5) dx

A: