65. Evaluate the integrals x³ In x dx. a. x² In x dx In x dx b. c. d. What pattern do you see? Predict the formula for x* In xd and then see if you are correct by evaluating it with a CAS. e. What is the formula for| x" ln xdx, n > 1? Check your answer using a CAS.

Q: Evaluate the following integral. e2 ( In (x?) -dx

A: We can use the substitution method to solve it.

Q: Evaluate the integral of x(x - 5)12 dx from 5 to 6

A: Given: ∫56x(x-5)12dx

Q: Evaluate the following integral. e5 dx 3x In x In (In x)

A:

Q: Evaluate the integral. In 2 2 e sinh 0 d0 - In 10

A:

Q: Q2: Evaluate the integral ° In xdx using by parts formula

A: We use integral by part

Q: Evaluate the integral. r 5 (In(x))² x3 dx

A: The integration by parts formula is ∫udv=uv-∫vdu

Q: Evaluate the integrals ∫coth x dx

A:

Q: Evaluate the integral of x(x – 5)^12 dx from 5 to 6

A:

Q: Evaluate the following integrals.

A: Given:

Q: Evaluate the integral: x ln x dx Choose the most appropriate answer. 승nz- +C ,6 -In x 6 36 x° (ln x)…

A: We have to evaluate the integral ∫x5 ln x dx

Q: (b) Consider the integral 16 – x² dx. Calculate the upper sum for this integral using n= 4…

A:

Q: Evaluate the following integrals.

A:

Q: Calculate the integral. (Use symbolic notation and fractions where needed.) e2x dx In 4 1 + e4x

A:

Q: Find the indefinite integral. 5 – ex e4x xp

A: the given integral is I = ∫5-exe4xdx

Q: 1. Determine whether the following statements are true and give an explanation or counterexample. It…

A:

Q: Evaluate the integral. |, arctan(1/x) dx (: -) * + In( *) 9. 2 O +In 2 4 (÷ - *) *+ In V3 8 n + 4 9.…

A:

Q: Evaluate the integrals in ∫8 e(x+1) dx

A: ∫8ex+1 dx Put  x+1=t⇒1+0=dtdx⇒dx=dt

Q: 8. Evaluate the integral x-1 dx by interpreting it as an area.

A: Area

Q: Find the definite integral from x = 2 to x = 4. 4 S In(a²)dx 2 O 6 In(4) O -0.5 O -4 + 3 In(16) O…

A: Let I is the value of given Integral.

Q: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx

A:

Q: Find the indefinite integral L 교리ln(2x)dz 4 O In(4) O None of the Above

A:

Q: Evaluate the following integral 5(ln æ)º dx| V(In æ)° –5

A:

Q: Evaluate the following integrals: (3" – e") dx A 3* In(3) – e + C 3*+1 ez+1 +C x +1 x +1 3* - e" + C…

A:

Q: 4. Evaluate the following integrals. (a) / + 5 - +e-* )dx

A:

Q: Which of the following is true for the integral A. In 5-In(-2) B. In 5-In 2 C. -In 5+ In 2 D. In 5 +…

A:

Q: 1) The following formula is entry #26 in our textbook's Table of Integrals. u? du ="Va" +u° -…

A: Given the integral ∫x225+x2dxWe need to use the formulae ∫u2a2+u2=u2a2+u2-a22ln|u+a2+u2|+C

Q: (2х) dx a(In x) + cos(ln x)]² 10 In(3x) - (In(3.x)

A: We have to find the indefinite integral

Q: Calculate the integral. (Use symbolic notation and fractions where needed.) e6x dx -In 2 1 + el2x

A:

Q: Evaluate the following integrals: (3" – e") dx = -

A:

Q: Evaluate the integral using the methods covered in the text so far:                    ∫ (7 − e10x)…

A: Here we have to evaluate I=∫(7-e10x)dx

Q: Evaluate the integrals in ∫e-1/x2/x3 dx

A: ∫e-1x2x3 dx Put, -1x2=t⇒2x3=dtdx⇒1x3 dx=dt2

Q: Either evaluate the following improper integrals or show that it diverges. +oo 1 (i) - dx +oo (ii) 2…

A: We have to evaluate the given integrals.

Q: Evaluate the integral: S (in ce) dx = (8 ln(x))²dx 2 (x8) ( ×

A: Evaluate ∫lnx82dx=?

Q: Evaluate the following integrals. Reasonable work is expected! 1.) 4x²e" dx

A:

Q: Find the indefinite integral. | 6/wdw +C.

A:

Q: 4 Which of the following is true for the integral A. In 5-In(-2) B. In 5-In 2 C. -In 5 + In 2 D. In…

A: Solution no. (2)  Options (B) is correct

Q: 71. | (In x)³ dx.

A:

Q: Evaluate the definite integral. 1 dp. lo 1 + p2

A:

Q: Evaluate the following integral using Romberg's method by taking n =8: 'dx

A:

Q: 2.S x² -4 X -dx

A: Note: Asper company guidelines, we are supposed to answer the first question only. Kindly ask the…

Q: etermine the following integrals by using (IF) 1. S dx 4x2+4x+1

A: Topic:- integration

Q: Evaluate the integral. 9. e dx -6

A:

Q: a) Evaluate the integrals using a dx i) S16x2 1+16x?

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

Q: Explain why each of the following integrals is improper  integral -infinity to infinity  x2 e -x2 dx

A: Given Data The integral is ꭍ∞-∞ x²e x2 dx   When one of limit or both limit points of integration…

Q: What is the integral of 1/(x*sqrt(ln(x))) dx from 1 to e^2?

A:

Q: Evaluate the integrals in ∫e1/x/x2 dx

A: Our Aim is to evaluate the integral given below:-I=∫e1/xx2dx -(i)

Q: evaluate the given integral.

A: To evaluate the integral: ∫ x2e-xdx Formula used: Integration by parts: ∫uvdx=u∫vdx-∫dudx·∫vdxdx

Q: —3г — 7 What is the value of the definite integral dt? Enter your answer as an exact fraction if…

A:

Q: Evaluate the integral: x23 ln x dx Choose the most appropriate answer. 24 -In x 24 24 + C - 576 x24…

A: