(2x - 5)^ + (2x

Find the indefinite integral ∫((x^2)/(4x^3+9)) dx

Leya [2.2K]

Answer:

$\displaystyle \frac{1}{12} \ln( |{4x}^{ 3} + 9|) + \rm C$

Step-by-step explanation:

we would like to integrate the following indefinite integral:

$\displaystyle \int \frac{ {x}^{2} }{4 {x}^{3} + 9} dx$

in order to integrate it we can consider using u-substitution also known as the reverse chain rule and integration by substitution as well

we know that we can use u-substitution if the integral is in the following form

$\displaystyle \int f(g(x))g'(x)dx$

since our Integral is very close to the form we can use it

let our u and du be 4x³+9 and 12x²dx so that we can transform the Integral

as we don't have 12x² we need a little bit rearrangement

multiply both Integral and integrand by 1/12 and 12:

$\displaystyle \frac{1}{12} \int \frac{ 12{x}^{2} }{4 {x}^{3} + 9} dx$

apply substitution:

$\displaystyle \frac{1}{12} \int \frac{ 1}{u} du$

recall Integration rule:

$\displaystyle \frac{1}{12} \ln(|u|)$

back-substitute:

$\displaystyle \frac{1}{12} \ln( |{4x}^{ 3} + 9|)$

finally we of course have to add constant of integration:

$\displaystyle \frac{1}{12} \ln( |{4x}^{ 3} + 9|) + \rm C$

and we are done!

6 0

3 years ago

Charlie guesses that his dog weighs 34. 5 pounds. The dog actually weighs 32. 7 pounds. What is the percent error in Charlie’s g

expeople1 [14]

Percent error is the amount of error to actual value, in percent. The percent error in Charlie’s guess is approximately: Option D: 5.5%

<h3>How to calculate the percent error?</h3>

Suppose the actual value and the estimated values after the measurement are obtained. Then we have:

Error = Actual value - Estimated value

To calculate percent error, we will measure how much percent of actual value, the error is, in the estimated value.

$\rm Percent \: Error = |\dfrac{Error}{Actual value}|\times 100 \\\\Percent \: Error = | \dfrac{\text{(Actual Value - Estimated Value)}}{Actual value}|\times 100 \\$

(here |x| is such that it makes x non negative, thus, |-5| = 5, and |5| = 5)

For the given case, it is specified that:

Actual weight of dog = 32.7 pounds

Guessed weight of dog, by Charlie : 34.5 pounds.

Error = 32.7 - 34.5 = -1.8 pounds

Thus, percent error in Charlie's guess is calculated as:

$\text{Percent Error} = |\dfrac{-1.8}{32.7}| \times 100 \approx 5.5\%$

Hence, the percent error in Charlie’s guess is obtained approximately is given by: Option D: 5.5%

Learn more about percent error here:

brainly.com/question/25749180

3 0

3 years ago

8) A company sells small and large photo books. Each page of a small photo book costs

Dennis_Churaev [7]

38 pages of the book will cost $57.

Data;

number of page = 20
cost = $30

<h3>Proportions</h3>

To solve this question, we have to know the cost of one page of the book.

In the first scenario, 20 pages cost $30, let's find the cost of one page here.

$20 page = \$30\\1 page = x\\x = \frac{30}{20}\\x = 1.5$

We can confirm our answer here by testing with the second scenario;

$32 page = \$48\\1page = y\\y = \frac{48}{32} = 1.5$

Now can say that one page of the book cost $1.5, let's divide 57 by this to determine the number of pages

$z = \frac{57}{1.5} \\z = 38$

From the calculations above, 38 pages of the book will cost $57.

Learn more on proportions here;

brainly.com/question/18437927

8 0

3 years ago

Tim earns $31 after 2 hours, $46.5 after three hours,

olganol [36]

Answer:

Equation: y = 15.5x

Step-by-step explanation:

Given that:

Time earns $31 for 2 hours

$46.5 for 3 hours

$62 for 4 hours

We will find unit rate first.

Unit rate = $\frac{31}{2}$ = $15.5 per hour

Now,

Let,

x be the number of hours

y be the total money earned by Tim

Total earning = Per hour rate * Number of hours

y = 15.5x

Hence,

Equation: y = 15.5x

4 0

3 years ago

How do I find the domian in exponential function<br>

jeyben [28]

Answer:

For any exponential function, f(x) = abx, the domain is the set of all real numbers. For any exponential function, f(x) = abx, the range is the set of real numbers above or below the horizontal asymptote, y = d, but does not include d, the value of the asymptote.

Hope it helps!!!!

7 0

3 years ago

(2x - 5)^ + (2x – 5)^