Make an appropriate u-substitution and evaluate the integral using the given circled integral table. [ x In(2 + x°)dx TABLE OF INTEGRALSBASIC FUNCTIONSSu"+1+ Cn+11.u" du =10.a" du =+Cdu- = In \u| + C2.11.In u du — u In и — и + Сu3.e" du = e" + C12.cot u du = ln sin u| + C4.sin u du = - cos u + Csec u du = In |sec u + tan u|+C13.= In [tan (}7+ }u) | +c5.cos u du = sin u +Ccsc u du = In |csc u – cot u| +C14.6.tan u du = In |sec u| +C= In |tan u| + C-1sinu du = u sin- u +V1 – u² + Ccotu du = u cot- u + In v1+u? +C7.15.- V1 – u² + Csec-u du = u sec u – In Ju + Vu? – 1|+C8.cosu du = u cos u-116.I-tan-u du = u tan-u – In v1+u? + C17.и du 3 и сscu + In \u + Vu² – 1|+C9.Csc-I

Answered: Image /qna-images/answer/b6085e84-85aa-4be7-bf47-2d9c99a7c987.jpg

Answered: x In(2 + x³) dx

Math

Calculus

x In(2 + x³) dx

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: Compute P,(f,0)(x) for the following function: f(0) = 42, f"(0) = 23, f) (0) =19, f®)(0) = 17, f("(0...

Q: 3. a) Find the percentage error in computing u = Vx at x = 2.45, when x is 4 %3D b) | If Ax = 0.005,...

Q: Question 7 dx 7-9e-2x Using u-substitution and transforming the integrand, find du. Given: A 14e2xdx...

Q: „3x -dx be given. If u=e* + 2, then the resulting integral is e+2 Jf(u) du. Compute f (3). Let A 3 B...

Q: Prove that the sum of the first n natural numbers is given by this formula: n(n + 1) 1+2 +3 +. .. +n...

A: As per our guidelines, we are supposed to answer only one question. Kindly repost other questions as...

Q: Tauluole bnn vle Question 1: Find 2Ã – 3B, |2Ã – 3|, JÃ\, \B|, 2|Ã| – 3||\, where Á = and B = %3D

Q: Given: -dx. Using u-substitution and transformation of integrand, what is u and du? 3/x - 2x 3 (A) u...

Q: xp xy6x -x

A: The given integral ∫1x6x-x2dxThe integral formula,117. ∫duu2au-u2=-2au-u2au+C

Q: 6 du dx. Transforming the integrand, the result will be k , where k is a constant. What is u and k? ...

Q: Find the Maclaurin polynomials of orders n = 0, 1, 2,3, and 4 and th find the nth Maclaurin polynomi...

Q: Find the centroid along the y-axis of the plane area bounded by the equation y^2=4x, x=1 and the x-a...

A: Given curve is y2=4x ,x=1

Q: Differentiate the function by using the definition of derivatives. f(x + h) – f(x) f'(x) = lim h f(x...

Q: One model for the spread of a rumor is that the rate of spread is proportional to the product of the...

A: Let's find.

Q: Calculate F. dS where F = (3xy°, xe", zª) S is the surface of the solid bounded by the cylinder y? +...

A: Let's find.

Q: Use the formula for the binomial series: (1 +x)" = 1+ mx + + + -1) %3D = I+ Ei to obtain the Maclaur...

Q: B. Directions: Expand t Scoring Rubric: 3- The final ansv 2- The final ansv 1- The final ansv 0- No ...

A: = (12q+4r)12 Binomial Expression:(a+b)n =∑n=0nni a(n-i) bi(12q+4r)12: a=12q, b=4r=120(12q)12-0(4r)...

Q: u+1 Using u-substitution, the integral Jf(x)dx reduces to a new integral glu) du. If glu) = , evalua...

A: Given g(u) = u+1u and ∫f(x) dx = x + lnx-1 + C

Q: n2 - 6 with n5 + 6 Write an inequlity comparing for n > 1. n3 (Express numbers in exact form. Use sy...

Q: f(x)= (x-2)/(x^2-x+1)^2the intervals on which f is increasing or decreasing (d.) the intervals on wh...

A: Given functionfx=x-2x2-x+12We will answer sub-part c, d and e(c) the intervals on which f is increas...

Q: Question 20 tan (In |4x2|) -dx is b ln Jcos (In |(2x) D[+c.• The integral of What is b?

A: I =∫ tan(ln|4x2|)x dxln|4x2| = t14x2 ddx(4x2) dx = dt8x4x2 dx = dtdxx=dt2Hence, Integral becomes;I=1...

Q: Find an equation for the graph sketched below: 8- 4 3- -5 -4 -3 -2 2 3 4 5 -2 -7 8+ f(x) = %3D Quest...

Q: 1. Find the tangent to the curve given by the parametric equations: X = 1/t; y= VE e-t

A: Appliaction of derivative problem

Q: 3) A businessman ventures to put up a digital printing shop which caters to printing of t-shirts for...

A: Let the number of t-shirts that will obtain maximum gross return is = 50+x. In this case x t-shirts ...

Q: Please see the attached image to see the given. thank you (a.) the critical numbers of f (b.) all ...

Q: The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventua...

Q: Question 2 12x +1 dxp. (2x- 1)2 (3x + 2)² Evaluate:

Q: Use the difference a,41 - a, toshow that the given sequence (a, ] is strictly increasing or strictly...

A: We can solve the following problem as:- Here N= {1,2,3,.......n...}

Q: Does the following power series converge for all real values of x? n=1 O It converges for all real v...

A: We will do ratio test for convergence test

Q: 3x -dx be given. If 4=e*+2. then the resulting integral is f(u) du.compute f (3). e* +2 Let 2 (A 3 B...

A: We have to find value of f(3)

Q: The sequence

Q: Question 12 For the following function , find the equation of f-(x) and hence show that f({=}) = f (...

Q: Is the series convergent or divergent? Explain in minimum of two sentences. +00 n2 – 1 n2 +1 Un n=1 ...

Q: Find dy/dx 1. sin^−1(xy) = cos^−1(x − y) 2. sec^−1(2y cos x) = x^y

Q: Calculate F. dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the plane...

A: We have to find double integral of F. ds

Q: show that for positive epsilon, |x-4| |3x-12|<e

A: a⇔b implies if a holds then also b holds and vice versa.

Q: 8 プ+5

Q: Followings are given for f(x) function and its derivative f' (x) Sf(0) =1 f' (0) =5 |F(2)=3 f' (2) =...

A: The given problem is solved below in detail.

Q: What is f'(x) given the integral function f(x) = cos(e“)d u? %3D O rm = 3x cos(e) O f'(x) = 3x cos O...

Q: tan²(x – 2) +2 sin(x – 2)4 Evaluate: lim

Q: Determine the equation (both standard and general) of the following conic sections based on the cond...

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other...

Q: ergence and the interval of convergence. Test for Absolute Convergence to the given series. The

Q: Determine whether the series converges. k=1

Q: 2. Divide the class into groups of 10. Measure the height of each member. Find the sampling distribu...

Q: Given: / 5x2 tan(3x³) dx. Ifu=3x°, then the resulting integral is Jf(u) A B none of the choices 5 18...

Q: Problem Set A (1) For the function f(x)=1- 1x+2 find the following: (i) f(-x) (ii) f(x +k)

Q: 5x² tan( 3x³) dx. If u= 3x³, then the resulting integral is Jf(u) du. Find . 5/2 A 18 5/2 18 5 18 D ...

Q: Use sigma notation to write the Taylor series about z = 1, for the function. 3 In z; z0 = 1 k =

Q: Question 21 sin 3x Given: dxWhat is the appropriate formula to find the integral? cos2 (3x) (4- 3 se...

Q: Situation 3: Find the area enclosed by the graph of the curve x^2+8y^2+16 = 0, the x-axis, the y-axi...

A: according to our guidelines we can answer only three subparts, or rest can be reposted.

Q: Consider the following sequence: 5" {an} = n=1 An+1 Use the ratio to show that the given sequence {a...

A: Given sequence an=5n2n2n=1+∞

Question

Make an appropriate u-substitution and evaluate the integral using the given circled integral table.

TABLE OF INTEGRALS
BASIC FUNCTIONS
S
u"+1
+ C
n+1
1.
u" du =
10.
a" du =
+C
du
- = In \u| + C
2.
11.
In u du — u In и — и + С
u
3.
e" du = e" + C
12.
cot u du = ln sin u| + C
4.
sin u du = - cos u + C
sec u du = In |sec u + tan u|+C
13.
= In [tan (}7+ }u) | +c
5.
cos u du = sin u +C
csc u du = In |csc u – cot u| +C
14.
6.
tan u du = In |sec u| +C
= In |tan u| + C
-1
sin
u du = u sin- u +V1 – u² + C
cotu du = u cot- u + In v1+u? +C
7.
15.
- V1 – u² + C
sec-
u du = u sec u – In Ju + Vu? – 1|+C
8.
cosu du = u cos u
-1
16.
I-
tan-u du = u tan-u – In v1+u? + C
17.
и du 3 и сsc
u + In \u + Vu² – 1|+C
9.
Csc-I

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Integral of cos2x on [0, infinity]
Area under the curve xy = -1 from x=1 to x=2
1. Find the volume generated by revolving about the line y = 0 the area under the arch of the sine curve y = sin x from x = 0 to x = π 2. Find the volume of the solid generated by revolving about y =1 the area bounded by the curve y = e^x , OX and the lines x = –1 and x = 0. 3. Find the volume of the solids of revolution generated when the region bounded by the curve y = x^2 , the x – axis and the lines x = 1 and x = 2 is revolved about the x – axis.
Green’s Theorem for line integrals Use either form of Green’sTheorem to evaluate the following line integral.
Find the firsst derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and the first partial derivative fx, fy, and fz of (x + yw )2 – ez – 2 = 0 and f ( x , y, z ) = 2xyz + tan x + y sin z Make the solution detailed and clear IN A PAPER.
Area under the curve y = 4 - x2 from x=-3 to x=3
How does Riemann integral work geometrically, the process of finding the area under a curve?
Dete‎rmine if f (x, y) = ={(xsi‎n3y)/(x‎2+y6), (x, ‎y) ≠ (0, ‎0) ={1, (x, y) = (0, 0) is‎ co‎ntinuous at (0,‎ 0)
Use Green's Theorem in the form of this equation to prove Green's first identity, where D and C satisfy the hypothesis of Green's Theorem and the appropriate partial derivatives of f and g exist and are continuous. (The quantity ∇g · n = Dng occurs in the line integral. This is the directional derivative in the direction of the normal vector n and is called the normal derivative of g.)
fomular f(x) =tanx/x and has a hole at x=0 prove algebricaly that it has a hole at x=0
Sketch the direction field of the differential equa tion.Then use it to sketch a solution curve that passes through thegiven point. y' = x - xy , (1,0)
2 : Let F = (2x cos(x^2 + y^2), 2 + 2y cos(x^2 + y^2)) and C be the curve joining(-1,-1) to (-1,0) by traveling on the curves y = x^3 from (-1,-1) to (0,0), theny = x^2 from (0,0) to (1,1) and finally on y = − 1/4 (x + 1)(x − 3) from (1,1) to(-1,0). Evaluate∮C F · dr