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
Luden [163]
2 years ago
14

Find the indefinite integral using the substitution provided.

Mathematics
1 answer:
Nady [450]2 years ago
4 0

Answer:  7\text{Ln}\left(e^{2x}+10\right)+C

This is the same as writing 7*Ln( e^(2x) + 10) + C

=======================================================

Explanation:

Start with the equation u = e^{2x}+10

Apply the derivative and multiply both sides by 7 like so

u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\

The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)

This way we can do the following substitutions:

\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\

Integrating leads to

\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\

Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.

To verify the answer, you can apply the derivative to it and you should get back to the original integrand of \frac{14e^{2x}}{e^{2x}+10}

You might be interested in
What is the sum of all measures of the interior angles of a regular pentagon?
Ugo [173]
There are 540 degrees total in the interior angles of a regular pentagon.

Just so you know, the total degrees of interior angles goes up by 180 degrees.

A triangle is 180 degrees, a quadrilateral 360, and a pentagon 540.
6 0
3 years ago
Mark's brother is 5 years older than Mark. Their combined ages add up to 23. How old is Mark?
anygoal [31]

Answer:

Mark would be 9

3 0
3 years ago
Read 2 more answers
What does this number apply to??
topjm [15]

Hey there!

The opposite of the square root of 25 is -5, and this is an <u>integer and a rational number and a real number.</u>

<u></u>

Hope it helps and have a great day!

4 0
3 years ago
Read 2 more answers
Which graph represents a function?
Roman55 [17]

Answer:

Graph B represents a function.

Step-by-step explanation:

Graph B is a quadratic function. y = x^2

5 0
3 years ago
Sam is packing crates that can hold 20 pears, and Josie is picking crates that are holding 6 pears. If they must pack the same n
kompoz [17]

Answer:

the answer would be 3 packs of 6

7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the Calculate
    14·2 answers
  • Is the quotient 2.7 ÷ 3 greater than or less than 1? Explain plzz!!!
    9·1 answer
  • PLZ HELP MEEEEEEEHHHHH
    15·2 answers
  • At which value(s) of x does the graph of the function f(x) have a vertical asymptote?
    9·1 answer
  • What is the unknown number ( +4)+59=70 i think it is 7
    13·1 answer
  • What are some non-price level factors that cause the aggregate demand curve to shift left or right (and in which direction will
    8·1 answer
  • What value of x makes the equation true?<br><br> a -3<br><br> b -1<br><br> c 3<br><br> d 1
    11·1 answer
  • Find the missing angle. ​
    12·1 answer
  • Simplify to a form a√ b
    9·1 answer
  • Write an expression for the sequence of operations described below.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!