Given that dx = 2 In|x + 1| – 2 In|x – 1|+c ,find dx = x² – 1 x² – 1 (a)–In9 (b) In9 (c)ln3 (d) –In3 (e) None

Q: dx 3. If 8c²xy = (x² - y2)2, find- dy

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Q9/ find the integration ſe^( (2x) ^3-1) x2 dx? * 1 а- 6. e2x* -1+c 1 b- e2x3 +C 1 .2x3–1+

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Q: -(3x² + 10)e¯= d Evaluate dx (3x² + 10)e¯ª at x = 0. d (3x² + 10)e dx x=0 II

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Q: for all of dx 1- y = xvInx 2- y = 3 x(x-2) x²+1

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Q: Find for all of : dx 1- y = xvInx x(x-2) x²+1 2- y =

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Q: d. (2xy*ev + 2xy3+ y)dx + (x²y*e° – x²y² – 3x)dy = 0

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Q: e2x -dx =D 1+ex (A e2x + In(1+ e*) + c B 2e2x – In(1+ e*) + C © e2x – In(1 + e*) + C D ex- In(1+ e*)…

A: Integration

Q: dx 2*+1-5x+1 (a) (b) [ cosh*x dx, (©) Jarcsin x)²1-x² dx, (c) 10* [In(v + 1)]² v +1 (e) T20 -02 (d)

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Q: d²y dx² - dy - - 6y = 0, when x = 0, y = 0, and when x = 1, y = e³ dx

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Q: S For x 1/2 x-x3 dx and using the substitutionu=x1/2

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Q: d²y dy Solve: x2 dx2 + 3x+y = 4 cos (In x³) dx L: L:

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Q: Derive a formula for In x dx where a. nt-1 b. n=-1

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Q: dx 1. S 2x-x² dy 2. if y = x* (In x)? . dx 3. Sx³e-* dx .

A: We have to find the integration and derivative as asked in the given question.

Q: If y = (x+-) (2x – 3), then dy will be dx a (2x+) + (x = 3)(1 +) G++)(e - x2) + (; ++) = A. (2x +=)…

A: Given that                          y=x+1x2x-3

Q: d²y Find the general solution for- dx² dx

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Q: dy of x3 +v³ = 4 of X + dx Find O x? y² ,2

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Q: e2 1 dx x In x e

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Q: Let ƒ(x) = x3 - 3x2 - 1, x>= 2. Find the value of dƒ -1/dx at the point x = -1 = ƒ(3).

A: We will need inverse function theorem. Statement of the theorem is:

Q: So d e2x 0 e2-5 dx is equal to

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Q: bernoulli dy dx + X = - 9.5 -xᵒy

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Q: Q4. Evaluate : O (xy²) dx dy -√1-(x-1)²

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Q: .2 -dædy In (x) ey

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Q: The S(e3x + 3x°) dx is { A }-e3* + 3xe + C e 3x 3xe+1 {C} 3e3* + + C { B }e* + e ln x 3xe+1 + C e+1…

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Q: Determine dy/dx y = (In 2x) - (ln(3x + 1)) 1 3x²+x 3x 1 None of the choices 1 3x²-x

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Q: Find the formula for df-1 /dx. f(x) = (1 – x)3 1 O A. 3x2/3 О В. 1-х1/3 Ос. -3(1- х)?

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Q: d S[e-In(2t+1)]dr. find g(x) - dx A e-In(2x+1) 2 B (2x + 1)² (2x + 1)² (2x+1)² If g(x) = D

A: We have to find out the derivative

Q: N= 8%° + 3s $1

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Q: dx is is equal to: 2x/4-(2x)2

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Q: d²y 1. dx² - dy - 6y = 0, when x = 0, y = 0, and when x = 1, y = e³ dx

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Q: of dx forf = 3x² y² – 4.x³ y Q2. + -

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Q: dy Find for all of : dx 1- y = xvInx 2- y = 3 x(x-2) x2+1

A: See the details solution in below

Q: SSS(x² + y²) dV where E lies between x² + y² +z² = 4 and x² + y² + z² = 9

A: E

Q: Inx+1 dy will be dx If y = then 2x3 – 3x' (2x³ – 3x) +1) –- (In x + 1)(6x? – 3) А. (2x³ – 3x)² (2x3…

A: Using derivative rule of (u/v),

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

A: solving given DE by separation of variables.

Q: A. Evaluate Inx dx. 2x B. Evaluate [(7x-10)dy dx. 0 x?

A: Note: Since you have posted multiple questions. We will solve the first question for you. If you…

Q: Q2) Evaluate the integral x3 dx 3 a *0.

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Q: In Prob. 1-38. Find dy/dx.

A: Given; y=e2x+3.

Q: Integrate the function. 3x? +7x- 18 dx x(x- 3)(x +2) |x°(x = 3) | O A. In +C (x +2)2 x°(x +2)* О В.…

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Q: If ƒ x Inx dx = x² In x – S f(x)dx, what is the value of , 4f (x)dx?

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: If S x²+x-2 (x2-1)(2x-x²) dx AS + Bf f(x) dx + D f g(x) dx, then x dx can be resolved into A ...

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Q: Find the antiderivate of dx/(x2+4)3/2

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Q: find dy/dx.x^-4/4 - x^-3/3 +x^-2/2 -x^-1 +e

A: We have given,

Q: Solve dx/dt+3x=e^-2t given that x=4 when t=0

A: dxdt+3x=e-2t Comparing with dxdt+Px=Q, we get P=3  &  Q=e-2t Now integrating factor is, I.F=e∫P…

Q: 2. Find b such that dx 1+x2 3

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Q: 7. Find for x2 + y² = y dx 2x а. 1-2у 2x b. 2у-1 с. 1-y d. y-1 e. None of the above

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Q: Let ƒ(x) = x2 - 4x - 5, x> 2. Find the value of dƒ -1/dx at thepoint x = 0 = ƒ(5).

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Q: 1. Use algebraic manipulation and (if necessary) u-substitu- tion to integrate the function. (a) /…

A: Hey, since there are multiple questions posted, we will answer the first three subparts of the…

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)? dx y logy x

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.