d. En=2 (-1)" %3D2 Inn e. 2n2+1

Q: a dy ピ+3

A: Given

Q: (b) Guess the value of dx when n is an arbitrary positive integer.

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Q: S. S. dy dx

A:

Q: (» — у + 3) da — (ӕ — у) dy — 0

A: Exact differential Equation: A differential equation of the form M dx + N dy=0 is said to be exact…

Q: S, (x3 + e*) dx

A:

Q: S- VE + 4) dx b)

A: We have to evaluate given integration ∫5x4-x5+4dx

Q: 19. csc (x) dx

A:

Q: Evaluate S 2y²sinxy dy dx

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Q: 5. S dx

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Q: 2. S 22+3x dx = 4 ( +c In 8.

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Q: D) Find S e5x+2 dx

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Q: e)S 2х-4 dx х3+5х

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Q: 2.S Ver eax dx Sve

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Q: 9) Sexte*dx

A:

Q: S se ex dx

A: LetI=∫sec3(x)dxI=∫sec2(x)sec(x)dxApply integraion by…

Q: 17. 2x√/x dx 18. de xVx S

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Q: Solve the IVP: dH/dx 3H when H(0) = 1

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Q: S. dy |1+5

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Q: 5) S dx X5V9X2-1

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Q: dy ー1

A: Given:

Q: 2 16e2=" dr dy 0.

A: Given:- Evaluating the integral by reversing the order of integration ∫02∫y216 e2x2 dx dy

Q: dx -=? S 3+2cosx

A: Given that a integration problem and we solve it by using general property of integration. We know…

Q: d) S 2xe* dx

A:

Q: e*Vex-1dx ex+3

A:

Q: In r dx 7.)

A:

Q: (#2) S 3xsin(4x)dx =

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Q: Evaluate: (4) S esc" (a) (2x +1) dx C6) Syos y dy

A:

Q: Find ∫ e5x+2 dx

A: This is a simple problem of antiderivative (also called integration). Here we are going to use…

Q: 5) ye"dx = (4 + e²^)dy

A: Given the differential equation

Q: (23×e¬*)dx

A:

Q: S dx 4+e*

A: follow next step

Q: S 3x³y dx

A:

Q: 15. S 4cot 5* csc25x dx

A:

Q: 6) S dx

A: We apply substitution rule for solving the integration

Q: dx a) S 19-x²

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

Q: 3. fesec'e Vran e* + 2 dx

A:

Q: e2y (е) dy |19+ edy)

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Q: a) Só xv4 - x2 dx

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

Q: dy 12

A:

Q: 3. S V5 + Vx dx

A: Given the indefinite integral I=∫5+xdx           .......(1)

Q: Q13) S 3+eZx dx

A: we can solve this as follows:

Q: S_a² – 1)*dx 7.

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: S4tan3 (пх + 1)dx

A: ∫ 4tan3πx+1dx=4·∫tan3πx+1dxLet u=πx+1.=4·∫tan3u1πdu=4·1π·∫tan3udu=4·1π·∫-1+sec2utanuduLet…

Q: Sí Si (3x² + 4y³)dydx

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Q: In 4 e2x dx 10)

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Q: 4. S° e*x²dx

A: Integration by parts: ∫f.g dx=f∫g dx-∫dfdx.∫g dxdx Given integral is: I=∫0∞e-xx2dx Let us evaluate…

Q: 11. S ye-y°dy

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Q: S xVx – 1 dx =

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Q: Vsin² 2x dx =?

A: Given ∫02πsin2 (2x) dx Remember sin2 (2x) is always positive. Thus, sin2 (2x) should be positive for…