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
anyanavicka [17]
3 years ago
8

Evaluate the following integral. Integral from nothing to nothing StartFraction 3 e Superscript x Over e Superscript 2 x Baselin

e plus 2 e Superscript x Baseline plus 1 EndFraction dx∫ 3ex e2x+2ex+1dx Integral from nothing to nothing StartFraction 3 e Superscript x Over e Superscript 2 x Baseline plus 2 e Superscript x Baseline plus 1 EndFraction dx∫ 3ex e2x+2ex+1dxequals
Mathematics
1 answer:
dem82 [27]3 years ago
4 0

Answer:

\int \frac{3e^x}{e^{2x}+2e^x+1}dx=-\frac{3}{e^x+1}+C

Step-by-step explanation:

To find this integral \int \frac{3e^x}{e^{2x}+2e^x+1}dx you must:

1. Take the constant out:

3\cdot \int \frac{e^x}{e^{2x}+2e^x+1}dx

2. Factor {e^{2x}+2e^x+1}=(e^{x}+1)^2

3\cdot \int \frac{e^x}{\left(e^x+1\right)^2}dx

3. Apply u-substitution u=e^x+1

3\cdot \int \frac{e^x}{\left(u\right)^2}dx

u=e^x+1\\du=e^xdx\\dx=\frac{du}{e^x}

3\cdot \int \frac{e^x}{\left(u\right)^2}\frac{du}{e^x} \\\\3\cdot \int \frac{1}{u^2}du

3\cdot \int \:u^{-2}du

4. Apply the Power Rule \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1

3\cdot \frac{u^{-2+1}}{-2+1}

5. Substitute back u=e^x+1

3\cdot \frac{\left(e^x+1\right)^{-2+1}}{-2+1}=3\cdot -\left(e^x+1\right)^{-1}=-\frac{3}{e^x+1}

6. Add a constant to the solution

-\frac{3}{e^x+1}+C

You might be interested in
What is the surface area of a rectangular prism that has a height of 5 cm, a width of 10 cm, and a depth of 4 cm?
Ket [755]

Option C: 220 \ cm^2 is the surface area of the rectangular prism

Explanation:

The height of the rectangular prism is 5 cm

The width of the rectangular prism is 10 cm

The depth of the rectangular prism is 4 cm

We need to determine the surface area of the rectangular prism.

The surface area of the rectangular prism can be determined using the formula,

A=2(w l+h l+h w)

Substituting w=10 , h=5 and l=4 in the formula, we get,

A=2 \cdot(10 \cdot 4+5 \cdot 4+5 \cdot 10)

Multiplying the terms within the bracket, we have,

A=2 \cdot(40 +20+5 0)

Adding all the values within the bracket, we get,

A=2 \cdot(110)

Multiplying, we have,

A=220

Thus, the surface area of the rectangular prism is 220 \ cm^2

Hence, Option C is the correct answer.

4 0
3 years ago
Read 2 more answers
What is the decimal representation of seven hundredths? A. 7. B. 700. C. 007. D. 07
Paraphin [41]

Answer:

C

Step-by-step explanation:

6 0
3 years ago
If two cards are randomly drawn from a standard 52-card deck, what is the probability that both cards are hearts?
Anettt [7]

Answer:

26

Step-by-step explanation:

You have to divide the two numbers, which are 2 and 52

5 0
3 years ago
WILL GIVE BRAINLIEST AND 20 POINTS!
lianna [129]

Answer:

2.6

Step-by-step explanation:

24 ft. divided by 9 is 2.6666666666...

5 0
3 years ago
Read 2 more answers
PLS HELPP I WILL MARK BRAINLIEST!!
Tpy6a [65]
The answer is 2 first you add then multiple
8 0
3 years ago
Read 2 more answers
Other questions:
  • Find an ordered triple to represent u in u=6w+2z if v=(4,-3,5), w=(2,6,-1), and z=(3,0,4).
    10·1 answer
  • Layla wants to build a wooden box with the volume of 45cubic centimeter. She started with a width of 3cm and a height of 3cm . H
    12·2 answers
  • A rectangle has a length of 16 feet and a width of 12 feet. Find the area of the rectangle in square feet.
    11·1 answer
  • Angles A and B together create a 90° angle. ∠A = 4x −10 and ∠B = 2x − 20. Find the angle measures (what will
    15·1 answer
  • How do I graph this?
    7·1 answer
  • Plz help and yes i am lazy but helpppp
    14·1 answer
  • What is the value of x in the figure? Enter your answer in the box.<br> 1450<br> (2x + 15)<br> x=
    13·1 answer
  • Solve each equation by taking square roots NEED FHIS ANSWER ASAP ILL GIVE BRAINLIEST
    15·1 answer
  • 1. Write a division sentence that tells what the<br> model represents.
    15·1 answer
  • There is a part c I will have to send it in the text there is not enough room
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!