3. | (9x? – 4x + 1) In xdx (A) 4 ln 2 19 2 (B) 18 In 2 – 7 - (C) 18 In 2 – 5 (D) 36 In 2 – 18

Q: H(x)= In(x+2)

A: our objective is to find x

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

A: To find the dy/dx of the given function

Q: 2 Evaluate the definite integral: 1+ 4x²

A:

Q: 7. Determine the integral| 2+1

A: The given integral,    ∫x dxx2+1

Q: 5. Find the indefinite integral 6.x²dx (2x³ + 7)3/2

A: The solution for the above question is as shown below.

Q: a=t). CTaylon Serie) 2-X Ln +x) (MacLurinSeries

A: We need to find the Taylor series of f(x)=12-x at a=1. Taylor series of function fx at a is defined…

Q: b 1+ e2x Evaluate the integral. ex xp 1 + e2x

A: Given that: ∫01ex1+e2xdx

Q: Find [4x³ (In x)² dx. O A. 1.4 X x In²x + In x + O B. x² ln² x - ln x + O C. x ln x O D. x ln x X 2…

A: Note : according to our gauideline, i can solve oy first so please reroute the remaining question.…

Q: To evaluate the integral 1. 7 64 + x² -dx,

A:

Q: |(In 6x)2 dx ОА. x(In 6x)2 - x(In 6x) + x + C В. x(In 6x)2 + 2x(In 6x) - 2x + C с. x(In 6x)2 - 2х(In…

A:

Q: 28. Evaluate the integral. x5-5x+4 x2

A: Indefinite integral: - The term "indefinite integral" refers to an integral that has no upper or…

Q: 3. Sum of coefficients of terms which contains integral powers of x in the expansion (2+ /x )30 is-…

A: We have to find sum of coefficient of terms which contains integral power of x:

Q: -25 Evaluate the integral: dax x²Vx2 +25

A:

Q: 2. f(x) = In 3r on [1,4 with n =5

A:

Q: 1 ER=1 (- 100 k%3D1 2k+1

A:

Q: 3 a2 Calculate the integral: da (*- 9)2 (x+ 9)

A: ∫3x2x-92x+9dx=3·∫x2x-92x+9dxTaking partial fraction…

Q: 5. Evaluate the integral. x+7 (x-6)(r-2)*a

A:

Q: Evaluate In x dx x3 А. In x x3 1 In x 2x2 1 + C 4x2 В. In x dx 1 1 x3 In x - 2x2 4x2 + C С. In x dx…

A:

Q: Evaluate the indefinite integral S(z -9-dz 를-9z + 듣 +C 4x4 중-9z + + C 222 - 9x + 7lnx³ + C - 7 9x -…

A: First we write each term using exponent

Q: 14. Find the indefinite integral. 7 49x xp- 13-7x8

A: Given integral is

Q: 27) 5 1 dx √x²- A) in (x+2+25+C In 5+X In +C 10 5-x nt B) +C X+5 D) (x+12-25374c In +C

A:

Q: Evaluate the indefinite integral. бх + 7 +C. || x2 +1

A:

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

Q: 6) calculate In (2e°)= 11 2= 0.7n 3= 1. || ln5=1.6n7=20 %3D n(2e°)=X L ex =In 2

A:

Q: Evaluate the improper integral : [* 4x°e=9¤*•

A:

Q: lim In(12x+ 1) csc(4x) A) 0. B) 1. C) е. D) 3. E) 0.

A:

Q: Find an integral expression equal to: 3 2 +3 lim k=1

A: The given sum is, S=limn→∞∑k=1n2nk3+32nS=limn→∞∑k=1n0+2-0nk3+32-0n⋯⋯1   According to the definition…

Q: What is g'(æ) when g(æ) = ln (3x³ +2)? Select the correct answer below: O In (9a2) 1 33+2 O 3z+2 9x2…

A:

Q: Evaluate the definite integral. '1 3 + 7t³j+ Vik) dt /-1

A: Consider the given definite integral

Q: Evaluate the indefinite integral. -3.5 - 15t - 3t-¹)dt (-15-35-3t-1)dt = 1 4 +²√t - 2 In t+c (Type…

A:

Q: 1 Find xIn(x15) dr. xln(x!5) 1 а. xIn(x!5) 1 -In] In(x!5) |+ C 15 1 dx = In] x'5 |+ C b. xln(x!5) 1…

A: Use the substitution method and integrate the given expression.

Q: 6) Prove mathematically that (1 grad = 0.9 deg) %3D

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

Q: Evaluate the integral∫ (4 /√(4 - x2)dx.

A: Let, I=∫44-x2dx Substitute x=2sint  gives dx=2cost dt…

Q: Identify the smallest integral upper bound and the largest integral lower. 7. h(x) = x³ + 2x² – 7x –…

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: 9 In(z² – 1) dz

A: Given: ∫9lnx2-1dx

Q: Find all possible values of x such that In(x) + In(x + 1) = ln(2). If no such values of x exist,…

A: lnx+lnx+1=ln2

Q: 4. Compute the exact value of (-1)"(n+2) xn+1 Ln=0 2n+1 (nt1) 100

A: The geometric series formula is ∑n=0∞rn=11-r, where r<1. Break the numerator of the given…

Q: 2. Evaluate the indefinite integral. 8dx xln(2x)

A: topic - indefinite integral

Q: 1. Express into parital fraction. Hence evaluate y2 -4 *2-4

A: according to our guidelines we can answer only three subparts, or question and rest can be…

Q: Evaluate the integral.

A:

Q: Show that dx = x² – 8x In (7 + 4/3). -

A:

Q: 11. The integral of an(In|4x-12 dx is bln|sec(ln(2x)ª)|. What is b? A. 2 В. 2 С. 4 D.

A:

Q: Find the indefinite integral. S 8x In(3æ)dæ A. +C B. 8 ln(3x) +8x + C C. 8x ln(3x) –- 6x² + C D. 4r²…

A: To evaluate ∫8x ln(3x) dx...(1)

Q: 17. Evaluate the integral. n x)²dx

A:

Q: Find the indefinite integral J(-16r² – 4x + 6)dr. a. -12r-4x + 6r +C b. -4x*- 2r+ áx +c c. -4x-2r+…

A: Solve the following

Q: dx x In(x4) In x4+ C -In h (In x4) + C -In In x + C

A:

Q: k Ink is Ln=1 (k+1)3 In k а. k2 In k+ln 1 b. k3 In k+ln 1 с. k2 In k d. k3

A: Serie and sequence, limit comparison test

Q: solve. write your anS w ers in suentific (-3.4 x 10*) + (5.2 x 10*) © (6.812 x 102") + (4. 3 x 102)…

A:

Q: 8. The improper integral | 1. x²+2x+5 1.

A:

Q: 4x Evaluate the indefinite integral. 1ª + 1 IP-

A: The given integral is: ∫4xx4+1dx