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
ratelena [41]
2 years ago
11

Integral of 3a^2/1+a^6

Mathematics
1 answer:
Elis [28]2 years ago
5 0
The trick here is to use an appropriate substitution.  Let u=a^3.
Then du/da=3a^2, and du=3a^2da.

We can now make two key substitutions:  In (3a^2)da/(1+a^6), replace 3a^2 by du and a^6 by u^2.

Then we have the integral of du/(1+u^2).

Integrating, we get arctan u + c.  Substituting a^3 for u, the final result (the integral in question) is    arctan a^3 + c.

Check this by differentiation.  if you find the derivative with respect to a of arctan a^3 + c, you MUST obtain the result 3a^2/(1+a^6).



You might be interested in
In which quadrant does the point (-4,15) lie
Ivanshal [37]
Quadrant one

Hope this helped
7 0
3 years ago
What is the answer to this question with work I need it ASAS
PtichkaEL [24]

The answer is 7 3/4 inches.

I noticed the word "train" in the problem and I knew I had to help you! :)

6 0
2 years ago
in a coin jar, there are 45 nickles. the number of pennies and nickles together equal the number of dimes. there are 2 quarters
fredd [130]

Answer:

45 nickels

30 quarters

60 dimes

15 pennies

Step-by-step explanation:

Quarters:

45÷3=15

15×2=30

Dimes:

30×2=60

Pennies:

60-45=15

HOPE THIS HELPS!!!!!:)

3 0
3 years ago
Which term would be combined with the constant +2 in the expression -8x^2 + 3x + 2?
Naddik [55]

The answer to this question is NONE OF THE ABOVE



you would take each answer and add 2 to the end of it, then factor

8 0
3 years ago
Read 2 more answers
What is the solution of -4(8-3x)>or=6x-8?
Illusion [34]

Answer:

-4(8-3x)>or =6x-8

Step-by-step explanation:

open d bracket

-32+12x >or = 6x-8

collect like terms

12x-6x >or =-8+32

6x = 24

divide both sides by 6

x= 4

8 0
3 years ago
Other questions:
  • Finn bought 2 packs of stickers. A friend gave him 4 more stickers. Now he has 24 stickers in all. How many stickers were in eac
    14·2 answers
  • Identify the expression for calculating the mean of a binomial distribution.
    7·1 answer
  • The equation y = log b^x<br> is equivalent to the exponential form
    14·1 answer
  • What variable expression represents the phrase "the difference of twice a number and 3"?
    5·2 answers
  • Find the slope of the line whose equation is 7x-2y=4
    10·2 answers
  • Susan determined that the expression below is equal to 7.59
    7·2 answers
  • Im using all my points for this pls help
    15·2 answers
  • Reflect quadrilateral SQRT over the y-axis. Then translate the new quadrilateral 3 units to the right. What are the coordinates
    9·2 answers
  • For the following exercises, solve each inequality and write the solution in interval notation.
    5·1 answer
  • What is the approximate value of x in the diagram below
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!