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
torisob [31]
3 years ago
7

Evaluate the definite integral. 1 x4(1 + 2x5)5 dx.

Mathematics
1 answer:
Nata [24]3 years ago
5 0

Answer:

Step-by-step explanation:

Given the definite integral \int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx, we to evaluate it. Using integration by substitution method.

Let u = 1-2x⁵ ...1

du/dx = -10x⁴

dx = du/-10x⁴.... 2

Substitute equation 1 and 2 into the integral function and evaluate the resulting integral as shown;

= \int\limits {\dfrac{x^4}{u^5} } \, \dfrac{du}{-10x^4}

= \dfrac{-1}{10} \int\limits {\dfrac{du}{u^5} }  \\\\= \dfrac{-1}{10} \int\limits {{u^{-5}du }  \\= \dfrac{-1}{10} [{\frac{u^{-5+1}}{-5+1}]  \\\\= \dfrac{-1}{10} ({\frac{u^{-4}}{-4})\\\\

= \dfrac{u^{-4}}{40} \\\\\\= \dfrac{1}{40u^4} +C

substitute u = 1-2x⁵ into the result

= \dfrac{1}{40(1-2x^5)^4} +C

Hence\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx = \dfrac{1}{40(1-2x^5)^4} +C

You might be interested in
When Tom found the difference −17 − (−12), he got −29. Complete the statement that explains what Tom might have done wrong.
ad-work [718]

Answer:

- 5

Step-by-step explanation:

Note that - (- 12) = + 12

Thus

- 17 - (- 12) = - 17 + 12 = - 5

It looks like Tom subtracted 12 from - 17, that is - 17 - 12 = - 29

8 0
3 years ago
Read 2 more answers
If you are driving at a rate of 55 miles per hour, about how many feet per second are you traveling?
Semenov [28]
55\ \frac{miles}{hour}\\\\
1\ mile\ =\ 5280\ feet\\
1\ hour=\ 3600\ second\\\\
55*\frac{5280}{3600}=80,7\frac{feet}{second}
3 0
3 years ago
Complete the equivalent fraction equation below. Blank over two equals two over blank equals blank over eight
podryga [215]
1 over 2 equals 2 over 4 equals 4 over 8.
Hope this helps! :)
5 0
3 years ago
A substance weighing 961 ounces decays at a rate of 3.2% PER HOUR. What is the weight of the substance after ONE DAY?
kifflom [539]
It would be 961 x (1-3.2(24)) and that would be 961(.232)= 222.952
6 0
2 years ago
Read 2 more answers
Help me out , please I forgot how to do this mathematics
netineya [11]

Answer:

C

Step-by-step explanation:

sorry if I'm wrong-

7 0
2 years ago
Other questions:
  • Kenneth drove 177.55 miles in 3 7/20 hours. what was his average speed
    9·2 answers
  • What is 100 decreased by 10%
    7·1 answer
  • 3 our of 5 picks are orange if 12 picks are orange how many picks are their in all
    6·2 answers
  • Laura has moved to a new apartment. Her schoolbooks comprising of different subjects are mixed in a bag during the move. Four bo
    13·1 answer
  • A snack bar offers chili and or cheese on its hot dogs for an additional fee. the owner kept track of the hot dog orders over th
    9·1 answer
  • At 7:00 p.m., there are 1,000 home-team fans and 700 away-team fans at a football game. After 7:00 p.m, 15 home team fans arrive
    14·1 answer
  • One type of plant root splits 44 times while growing in the ground. The number of new roots after each split can be modeled by t
    7·1 answer
  • Tessa bought stock in a restaurant for $103.00. Her stock is now worth $126.69. What is the percentage increase of the value of
    10·1 answer
  • Question 4
    5·1 answer
  • Divide g(x) = x^4 - 2x^3 + X + 3 by x+3
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!