5. Show that (x² + 1)e-* dx = -x²e-x – 2xe-x – 3e-x +C

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y * logy x *

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Q: 5. Evaluate the integral 2 c2x x2 (x² + 2y³) dy dx.

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

Q: 2- Find O for: y= In (x+5x) dx

A: Tpoic- Differentiation

Q: 4 18. Evaluate the indefinite integral / dx. 3 X,

A: Given integral to find ∫4x3dx To integrate this first take the constant out 4∫1x3dx Applying the…

Q: (a) Apply first principles, to calculate the differential coefficient of (x) = 5(3x²+2) when x = 3.

A: Solution a: Given function is f(x)=5(3x2+2) using first principle…

Q: Find d if z = log2 y - 6 logs y. In In 64 dz dz dy y In 2 In 5 dy y In 2 In 5 O Option 3 O Option 2…

A:

Q: Solve the differendialegimaition: (2x+e)dx + (xay co

A: Make some simplification and rearrange the given differential in exact form.

Q: Example 2: Find the particular solution of (x – y)dx + (3x+y)dy = 0 when x = 2 & y = -1.

A:

Q: If the function f (x) solves the initial value problem dy E (х + 1)-И dx -1/2 IT • cos(TX)

A: Givendydx=x+1-1/2-πcos(πx)

Q: d If g(x)=- -S*[e' - In (21+1)]dt, find g(x) Se dx 4 A (2x+1)² 4 B e+ (2x + 1)² Ⓒe* -In (2x+1) 2 D…

A:

Q: EXAMPLE 7 If it is known that f(x) dx = 12 and f(x) dx = 10, find f(x) dx. SOLUTION By a property of…

A: We have to solve

Q: 1: Evaluate the integral 3x - 1 (x + 4)(2x - 1) I -dx.

A:

Q: integral from 1 to 2 of (e1/x^3 ) / x4

A: To evaluate

Q: Find a ≤ b such that

A: ∫abx2-9dxApply the Sum Rule:…

Q: In +1- 2 dt, if we let V Vt+1-2, then dt is equal to t+1– 2, then dt is equal to A) None 4x³dx ©…

A:

Q: EXAMPLE 7 If it is known that F(x) dx = 14 and f(x) dx = 9, find F(x) dx- SOLUTION By a property of…

A:

Q: 1. Evaluate the integral |(x² - 5)e*dx 8.

A: Given that: ∫0∞ x2 -5e-3x dx To find: The value of the given integral. Let I = ∫0∞ (x2 -5)e-3x dx…

Q: 32. Find of In(7x² - 3x + 1). dx 14x-3 dy A. = dx C. = 7x²-3x+1 dy 1 B. = dx D. = 7x²-3x+1…

A: To find out the derivative.

Q: 1) Find dy/dt for if : y = log2 (81'n 2)

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

Q: e*dx e -x +1

A:

Q: 1. Evaluate the integral of x2 (3 - 2x) dx if upper limit = 2 and lower limit = -1. а. 12 b. -12 C.…

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Q: In 3 e'dt 0 ve Ve2t+4

A:

Q: 1 Find the most general antiderivative of the function x3 + 4x

A:

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y logy x * * -

A:

Q: 1. (a) Show that (x) x² is an explicit solution to dy X- = 2y dx on the interval (-∞, ∞). (b) Show…

A: An explicit solution is any solution that is given in the form y=y(x)

Q: 1. Evaluate 5 S Sx (x + 3x)dydx

A: Given, ∫05∫0x x(x + 3x) dy dx=  ∫05∫0x (x2 + 3x2) dy dx=  ∫05 ∫0x (x2 + 3x2) dydx= ∫05 ∫0x 4x2 dydx

Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

A:

Q: •1 cln(5) 1- S SmS) xy evx ´dydx r

A:

Q: 2 3. Evaluate the integral ||x dx -2 O 2 4

A:

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y * logy x |

A:

Q: S de x² –2 x+1 A x2 --x - In Ix + 11 + C C x2 +x - In Lx + 11 + C B x² -x + In Lx + 11 + C x2 +x +…

A: Given ∫x2-2x+1dx. The objective is to evaluate the integral.

Q: If g(x) = - - S^*[e'- In(2t+1)]dt, find g'(x) . dx A ex-In(2x+1) 4 B

A: We can solve this as follows:

Q: Evaluate the integral. 3x-7 (a) S- dx x2-2x-8

A: Answer and explanation is given below..

Q: 8. Compute using the trig. substitution S x2 -dx (1–x²)1/2

A:

Q: 8x + 1 10. Evaluate the integral / dx. 4.x2 + 12x + 10 11 (a) In |4.x2 + 12x + 10|| tan-(2x + 3) + C…

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Q: 7. Solve the following Cauchy-Euler equation d’y dx² dy +5x- +3y = In x. dx

A:

Q: (6) Find the indefinite integral (af* -3x +2 Fdx x+1 12x - 22x (bJ -dx 3x* -11x +15 x² + 2x +3 -dx…

A: Note: As per companys policy we should do maximum 3 subparts of a question.So, kindly post the other…

Q: 2. Evaluate the integral: 2xe-**dx -0

A: topic - integration

Q: 3. Find the integral x² +12x +12 dx x' - 4x

A: Given,            ∫x2+12x+12x3-4xdx

Q: 1. Evaluate the integral 2 dx x2 +4x + 20

A:

Q: 2. Test for exactness and find the complete solution of n dx + {In(2x – 2) + dy = 0 - (х-1)

A:

Q: 2. Solve the following problem 10 (хи — 2x2 — 5и?)dt max | 0, dx = x + 3u, x(0) = 6, x(10) free dt

A: We will use Euler-Lagrange equation to solbe the optimization problem.

Q: – 30 - Evaluate the integral: -d.x x2 Vx2 + 16

A:

Q: Find the general solution to 3 1 0 0 3 1X. -X= dt 0 2

A: We first find eigen values, then corresponding eigen vector to solve the given system as in next…

Q: If g(x) = — _*[e'-in(21+1)]dt, find g''(x) . - dx 2 A ex_ (2x + 1)2 B e* - In (2x + 1) 4 с ett (2x +…

A: Given:  g(x)=ddx∫-2xet-ln(2t+1)dt To Find: g"(x) Formula to be used: Fundamental theorem of…

Q: 1. Evaluate the integrals that converge: dx 2x ! dx (x2 + 5)3 b) a) 3-x - 00

A:

Q: Find 뿐 for the ry – ln(xy) = 1 0 뽈 ㅇ-볼 O 래 ㅇ-픕 following:

A: The given expression is xy-lnxy=1 we have to find dydx use the derivative formulas, ddxx=1…

Q: In ( x² + 3x -=-7) dx X-2 Evaluate the integral: Se Ⓒ + A x² 2 =+ + In|3x-6|+C ℗ +² +5x+3n|x-2/+C B…

A: To find out the integration.

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

A:

Q: Find the general solution using Reduction of Order: x2y''-xy'+y=0 y1=ln x

A: