1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
netineya [11]
1 year ago
6

Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) dx x(l

n x2)5
Mathematics
1 answer:
Pepsi [2]1 year ago
7 0

I'm assuming the integral is

\displaystyle \int \frac{dx}{x (\ln(x^2))^5}

We have

\ln(x^2) = 2 \ln|x| \implies (\ln(x^2))^5 = 32 (\ln|x|)^5

Then substituting y=\ln|x| and dy=\frac{dx}x, the integral transforms and reduces to

\displaystyle \int \frac{dx}{x(\ln(x^2))^5} = \frac1{32} \int \frac{dy}{y^5} \\\\ ~~~~~~~~ = \frac1{32} \left(-\frac1{4y^4}\right) + C \\\\ ~~~~~~~~ = -\frac1{128(\ln|x|)^4} + C

which we can rewrite as

128 (\ln|x|)^4 = 8\cdot2^4(\ln|x|)^4 = 8 (2\ln|x|)^4 = 8 (\ln(x^2))^4

and so

\displaystyle \int \frac{dx}{x (\ln(x^2))^5} = \boxed{-\frac1{8(\ln(x^2))^4} + C}

You might be interested in
What is 13 out of 25 as a percentage
elena-s [515]

Answer:

%52

Step-by-step explanation:

13/25 0.52 move decimal two places to left and add percent %52

5 0
3 years ago
Read 2 more answers
Tyreek Hill has scored 32 touchdowns in 59 games. If he continues at this rate, how many touchdowns will he score in the 2020 se
Romashka-Z-Leto [24]

Answer:

hi            

Step-by-step explanation:

6 0
3 years ago
A sweater is on sale for 20% off. A jacket is on sale for 15% off. The sale price for each item is $34.00. Which item cost more
SashulF [63]

The sweater cost more originally. It costs $2.50 more from jacket.

Step-by-step explanation:

Given,

Discount rate of sweater = 20%

Sale price of sweater = (100-20)% = 80%

Discount rate of jacket = 15%

Sale price of jacket = (100-15)% = 85%

Sale price of each item = $34.00

Let,

x be the original price of sweater.

y be the original price of jacket.

80% of x = 34

\frac{80}{100}x=34\\0.80x=34

Dividing both sides by 0.80

\frac{0.80x}{0.80}=\frac{34}{0.80}\\x=42.50

The original price of sweater is $42.50

85% of y = 34

\frac{85}{100}y=34\\0.85y=34

Dividing both sides by 0.85

\frac{0.85y}{0.85}=\frac{34}{0.85}\\y=40

The original cost of jacket is $40

Difference = 42.50 - 40 = $2.50

The sweater cost more originally. It costs $2.50 more from jacket.

Keywords: subtraction, division

Learn more about subtraction at:

  • brainly.com/question/10557938
  • brainly.com/question/10600222

#LearnwithBrainly

4 0
3 years ago
Has anyone taken Ap language and composition
soldi70 [24.7K]

Answer:no

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
2. If a, b are non-zero rational numbers, and c is a non-zero irrational number, what can we say about
topjm [15]
B lookkkdhdvdb svdbd dhd. She d. Did d. He r. He. Hebrbeue. I’m going uuuyyyyyyyywjd
5 0
3 years ago
Other questions:
  • (x + 2)² <br> Given: (x + y)² = x² + 2xy + y²
    11·2 answers
  • Give the equation of the line through the point (4, 5) with a slope of - 9/2
    12·2 answers
  • What is the inverse of f(x)=(x+6)^2 for x≥–6 where function g is the inverse of function f?
    5·1 answer
  • What is the volume of a cylinder? Give an informal argument for the formula.
    5·2 answers
  • 3 bananas cost $0.99. At this rate, how much do 5 bananas cost?
    11·2 answers
  • What is the value of y when X=10?
    5·1 answer
  • A number x subtracted from 9.8 is greater than -4.
    6·1 answer
  • I WILL GIVE BRAINLIEST TO CORRECT ANSWER
    6·1 answer
  • Find the area of each figure. <br> Please help!! I usually don’t ask for help I’m having trouble.
    6·1 answer
  • Suppose that there are 500 students in the school about how many of them study between 4.2 and 5.8
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!