Evaluate L S dx dy. O 1 2/3 1/2 O 2

Q: -3x dx. Evaluate O 4. 3e -3 OB. OC. O D. 3 OE e+1

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Q: Find dy/dx for the following       y=ln(x2 +1) 5

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Q: sp dy dx dz (1–z) Evaluate .

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Q: e ax dx

A: 1. Let In=∫xneaxdx. Use the integration by parts formula ∫udv=uv-∫vdudxdx to evaluate the integral…

Q: 1. Approximate dx using each of the following.

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Q: Integrate the following using ~2 x+1 2. dx

A: ∫12x+1xx-1dx

Q: FIND DY/DX OF THE FOLLOWING 5. y=csc Inx

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Q: 22. Evaluate So Si S dx dy dz.

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Q: and du = dx L dx = , we need to set u(x) = x-1 (x-1)

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Q: L{sinh 6t– cosh t

A: we have to find the value of L{sinh(6t)-cosh(t)}

Q: Evaluate Si S dz dæ dy 0. 4.

A: Here I am attaching image so that you understand each and every step.

Q: xe* dx Jo (1+x)

A: Given                                            I=∫01xex1+x2dx now,…

Q: S Le+6)dx (x+2)*

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Q: If y? In(x) = 5, find dy/dx. dy dx

A: This question is based on differentiation with respect to x.

Q: 5. Find (x +3)² dx, (be careful!) 5. e® + e¯ | cosh r de dx %3D

A: The complex form of integral can be converted to simple integral using integration by substitution…

Q: Evaluate the following integral. 3 5 e dz dx dy -2 4 1

A: Calculation:

Q: Suppose d a e R, where a > 0, a ± 1, what is (a*]? dx

A: Given,            Supose a ∈ R, where a>0, a≠1.To find : ddxax

Q: (In x)² dx, .3 te ato u a ? and dy

A: Integratipn by parts problem

Q: 3.) y tanʼxdx +ln* ydy = 0 dy_ (y?+4) Inx In (y?+4)Y 5) dx

A: y tan2x  dx + ln4y dy = 0∫-tan2x  dx =∫ ln4yy dy∫(1 - sec2x) dx  = ∫ t4 dt   (where, t = ln y)Hence,…

Q: find dy dx 15 In 4+ xe) 6

A: dlnax+bdx = a.1ax+b.

Q: Evaluate the given integral ∫ 2x/ e^5x dx

A: ∫2xe5x dx

Q: Use this information to evaluate 1 (1- e)| dx %3D x=1 et - 1

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Q: d Suppose a E R, where a > 0, a ± 1, what is- - [a*]? dx

A: We need to find ddxaxwhere a>0,a≠1

Q: 1 dx x(In x)*

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Q: Rewrite using the order dy dz dx. [L² dz dy dx = 5 5. O dy dz dx

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Q: :-'In²(Ine*)dx A In?x В Inx C Ine* D) Inx2 E None

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Q: Solve for the following integral: 1 -dx (e2x – 4)5/2

A: I=∫1(e2x-4)52  dxu=-2xdx=-12 duI=-12 ∫due-u-452v=e-u −4dv=-e-u du-dv(v+4)=duI=12∫1v52 (v+4) dv

Q: 1 dx is divergent True O False

A: Since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: d 55. Vcosh x +1 (cosh x + 1)-/2 sinh x dx

A: Given The function is f(x)=cosh x +1 .

Q: Suppose a E R, where a > 0, a # 1, what is[a"]? dx a" In(a) © xa²-1

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Q: 2. ye* dx + e*dy = 0

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Q: a) In(x+1)³ dx x+1

A: Given, ∫23ln(x+1)3x+1 dx

Q: d Suppose a E R, where a > 0, a + 1, what is [a*]? dx

A: We have to find derivative of ax

Q: Question 40 Evaluate V1+ a?dx dy O 2/2 3 O 2/3 O 112/2 3. O 1/3

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Q: find dy/dx x(х+1)(х- 2) (х*+1)(2х+3) 25) у%3 43) у%3D 1+(lin x)? 1+(ln x)?

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Q: Solve the folkowing di fferential equotions 1. xdy dx + dy x'

A: Firstly , we can solve for dydx. After that we can see that the equation is an homogeneous…

Q: Find 3 for 2 = In (xº dx Provide your answer below: +y¹).

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Q: 1 dx is finite -1 X Select one: True False

A: True

Q: Find d when y = 3 In(In(In(x))) dy dx

A: Here we can find the derivative as below

Q: 2. S dx I+,x

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Q: S 3* e*dx

A: Integration means addition it is used for adding continuous function which can't be added by simple…

Q: | (3e* + 1)? e* dx

A: Given integral, ∫3ex+12ex dx

Q: Evaluate 1- x? dx 0. by Simpson's rale with n=5

A: Here fx=x1-x2 The interval is 0,1 and n=5. Hence the interval is divided into 5 equal parts.…

Q: d Suppose a E R, where a > 0, a ± 1, what is[a*]? dx

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Q: e2: S dx 1+ex

A: Given the integral ∫e2x1+ex dx u = 1+ex  ⇒ ex = u - 1 du = ex dx By substitution method, I=∫e2x1+ex…

Q: a) I= [In(l+x)dx

A: We have to find out the integral

Q: S(a – x)°dx

A: We need to integrate given function.

Q: Q\ Find for y = tanh 1(coth(x)) dx O -2 O -5 -4 7. O O O O

A: