Question: a. Evaluate x ln x 2 dx using the substitution u = x 2 and evaluating ln u du. b. Evaluate x

a. Evaluate ∫ x ln x2 dx using the substitution u = x2 and evaluating ∫ ln u du.

b. Evaluate ∫ x ln x2 dx using integration by parts.

c. Verify that your answers to parts (a) and (b) are consistent.

Step by Step Solution

★★★★★

3.38 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a Let u x so that du 2x dx Then rmrdr 1 mudu umu u C x ln dx 1 ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Calculus Early Transcendentals Questions!

Q:

a. Evaluate tan x sec 2 x dx using the substitution u = tan x. b. Evaluate tan x sec 2 x dx using the substitution u = sec x. c. Reconcile the results in parts (a) and (b).

Q:

a. Evaluate cot x csc 2 x dx using the substitution u = cot x. b. Evaluate cot x csc 2 x dx using the substitution u = csc x. c. Reconcile the results in parts (a) and (b).

Q:

An integrand with trigonometric functions in the numerator and denominator can often be converted to a rational integrand using the substitution u = tan (x/2) or equivalently x = 2 tan -1 u. The...

Q:

Please briefly explain the solution and all steps, including substitution steps, triangles, and formulas used. Thank you! -2 x e sin (2 x) du Put 21 = u 7 2 dx = du + du = du 2 - 2X e sim (2x ) dx =...

Q:

1 Suppose we want to evaluate the definite integral, x(Ina)2 do using the substitution, u = In(x). Part 1. Re-write the definite integral in terms of the variable u and remember to use the limits of...

Q:

math Substitution in the Definite Integral Suppose we want to evaluate the definite integral, 1 3 ez2 dx using the substitution, u = 2 72 . Part 1. Re-write the definite integral in tern the variable...

Q:

Can someone please explain it to me ASAP???!!! This is integral by parts Evaluate 10 cos v 10x dx using a substitution followed by integration by parts. Use the integration by parts formula so that...

Q:

Please #27, 29, 31, 33, 35, 37, 39, 41,45, 57, 61, 69, 77 1-4 Evaluate the integral using integration by parts with the 9. f w In w dw 10. In x -2 . dx indicated choices of u and du. 1. (xedx; u = x,...

Q:

Please #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 1-4 Evaluate the integral using integration by parts with the 9. f w In w dw 10. In x -2 . dx indicated choices of u and du. 1. (xedx; u = x, du...

Q:

Please #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 1-4 Evaluate the integral using integration by parts with the 9. f w In w dw 10. In x -2 . dx indicated choices of u and du. 1. (xedx; u = x, du...

Q:

A ski resort is planning a year-end promotion by offering a Saturday night special for $109 per person. The high season rate for these rooms is $299. Management wants to hold some rooms for late...

Q:

Air enters a convergingdiverging nozzle of a supersonic wind tunnel at 1.5 MPa and 350 K with a low velocity. If a normal shock wave occurs at the exit plane of the nozzle at Ma = 2, determine the...

Q:

Assuming that X is a binomial random variable with n 5 10 and p 5 .20, find the probability for each of the following values of X: a. X 5 5. b. X 5 2. c. X 5 1. d. X 5 9.

Q:

4. Why has the cash balance increased during the year despite the company incurring a loss?

Q:

Suppose that f and t are continuous on [a, b] and differentiable on (a, b). Suppose also that f(a) = g(a) and f'(x), g'(x) for a

Q:

Find the limit. Use lHospitals Rule where appropriate. If there is a more elementary method, consider using it. If lHospitals Rule doesnt apply, explain why. lim 818 (In x) X

Q:

Find the critical numbers of the function. f(x) = 2x 3 + x 2 + 8x

Q:

Ratna Garments is thinking of changing its credit policy from net 30 to 2/15, net 40. Under current terms, Ratna's sales are Tk.28 million per year, collection costs are k.160 thousand, and bad debt...

Q:

conds stion Completion Status: Moving to another question will save this response on 4 Bank offers 4% interest for 3 months term deposits, 4% for 6 months deposits and 5% for 1 year deposits. What...

Q:

11. More on the corporate valuation model Praxis Corp. is expected to generate a free cash flow (FCF) of $11,865.00 million this year (FCF1 = $11,865.00 million), and the FCF is expected to grow at a...