Step 3 The integral 27 12xe-x? dx can be done with the substitution u = 2 X- and du = -2x dx. -2.x Step 4 With the substitution, we have 27 12xe-x2 dx eu du + С. %3D Submit Skip (you cannot come back)

Q: 1. Given y= [In(3x² +8)] dy find tan(6x) dx

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A: We need to solve the integral

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Q: Original Sound ff EXERCISE dy -x = x2 siny dy 3 -(-siny ANSWER: X = %3D

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Q: (a) /4 1+3 cos² 1 d.x; COST dx3B

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Q: (1+x° 2) 늪(cot-1 () - d dx 1-x,

A: Solution:To find:ddx cot-1 1+x1-x=?Formula:ddxcot-1x=-11+x2ddxuv=vu'-uv'v2

Q: Can i get help step by step please?

A: Given function is

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A: Since this is a multiple question, according to the Bartleby answering rule, only first question is…

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Q: Cos X -1 dx = ? 22n (a) -)". (b) (-1)". 22n+2 (2n).(2n)! n=1 (2n +2).(2n + 2)! n=1 22n+1 22n-1…

A: ∫02cosx-1xdx

Q: I+11z|10 dx=? O a. 2lna + arctan(x + 2) – In((x + 2)) + C O b. Inx? + 5arctan(x + 2) – In(1+ (x +…

A: ∫x2+11x+10x3+4x2+5xdx

Q: 1 tegral 2-2 dx eq" others

A: We have to choose the correct option according to the given information

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A: Consider the following integral: ∫2ex-3e-2xdx=2∫exdx-3∫e-2xdx=2ex-3∫e-2xdx Consider the following…

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Q: 4. Bernoulli's Equation 3dy – 4xy dx = 3x²y*e=2x² dx Зdу — 4xу dx

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Q: If x +y° = 28, find the value of 3 at the point (1,3). dx d?y The value of - dx (Type a simplified…

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Q: (х+2у — 1) dx — (2х + у + 5)dy %3D 0 IC:х — 1,у — —1

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Q: tegral 1 -r³e"la0 cos²e ,² dr sin@d0 ¢ do = x 32πα x = ? %3D

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Q: Solve the equation (2х + 6) (2y? + 3) dx + 4y(x? + 3x + 2) dy %3D 0

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Q: 6) S sech? (2x- 3) dx | ex-e-x 7) S ex+e-x 8) S(eax – e-ax) dx sinh x 9) S dx 1+cosh x 10) ſ csch? x…

A: Given

Q: 1. Do you need using substitution method to solve (x2 – 9)(2x)dx ? If yes, please identify u and…

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

Q: ich option is an antiderivative of Sar 3x cos(-2x) dx a. 3 9.

A: We will use integration by parts to find the answer.

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Q: Step 3 We must also convert xõ dx into an expression involving u. Using du = 9x³ dx, then we get x…

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Q: 16 ) d du -1 cos и — 1<и<1 dx V1 – u² dx

A: As we know that the differentiation properties:- chain rule: ddx(f(g(x)))=f'(g(x))g'(x)…

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Q: 6. Solve the initial value problem. ( tan (4y) - 1)dx + | 4x sec (4y) + dy = 0, y(0) = 1

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Q: (b) 6x Cos dx. (Hint: you might need to use integration by parts several times.

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Q: dy - x = x2 siny dx 3 -2 (-siny + cosy + Ce-y/2)* ANSWER: x = -

A: Note: Here, we shall solve Bernoulli's differential equation  dxdy-x=x32sin y instead of…

Q: Find dy/dx of: x3 - sin y = (1/x3) + tan-1 (ey) - π/4 Don't simplify the final answer.

A: Given:     To determine:

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Q: 34. e4x cos 2x dx

A: Solution:Given∫ e4x cos 2x dxFormula:∫udv=uv-∫vdu∫sin ax dx=-cos axa+C∫cos ax dx=-sin axa+C∫eax…

Q: Evaluate the integral. sin(10x - 2) dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (15pts) Identify (write down) the type of DE, and find the general solution. (y- 3x)dy = (x +3y)dx…

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Q: 1) I = ft e" dt 2) I = Se-2x sin 2x dx

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Q: Using the substitution x= X -3 and y= Y-3 show that the equation dy y+3 dx x+y+6 can be reduced to a…

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