What is the solution to 8x - 3(2x - 4) = 3(x

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

Malik wrote 18 ➗6 = 3. Which problem can he solve using this equation?

ki77a [65]

Answer: Anything for example:

Malik has 6 friend, he wants to equally give them some of the 18 cookies he back earlier that morning. How much will he give each person?

Step-by-step explanation: And the answer will be 3

6 0

3 years ago

Read 2 more answers

A coffee shop collected the following information regarding purchases from 110 of its customers 59 purchased coffee 39 purchased

Andrej [43]

Answer:

Let X be the number of customer purchased coffee

Let Y be the number of customer purchased donuts

Then $X\cap Y$ is the number of customer purchased both coffee and donuts

$X\cup Y$ is the number of customer purchased both coffee or donuts

The Number of customers purchased only Coffee:

Number of customers purchased only donuts =n(X -Y)

$n( X -Y) = n(X) - n(X \cap Y)$

n(X-Y) = 59 -16

n(Y - X) = 43

The Number of customers purchased only donuts:

Number of customers purchased only donuts =n(Y -X)

$n(Y - X) = n(Y) - n(X \cap Y)$

n(Y - X) = 39 -16

n(Y - X) = 23

The Number of customers did not purchase either of these items:

Number of customers did not purchase either of these items = $n(X\cup Y)^{\prime}$

First lets find $n(X\cup Y)$

$n(X\cup Y) = n(X) + n(Y) - n( X \cap Y)$

$n(X\cup Y) = 59 + 39 - 16$

$n(X\cup Y) = 82$

$n(X\cup Y)^{\prime}$ = $110 - n(X\cup Y)$ = 28

5 0

4 years ago

A bookstore has a sale:

ira [324]

16.00 I think by 40% for one book but for two is 80%

7 0

4 years ago

Homework problem #7: 24567389+35432611=what there is soo much regrouping, could someone show me how to do it?

Natasha_Volkova [10]

Answer:

$24567389+35432611 =60000000$

Step-by-step explanation:

Given

$24567389+35432611 =$

Required

Solve

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

The numbers in parentheses are carried from previous sum

Start from the right

$9 + 1 = 10 \to$ Write 0, carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0

$8 + 1 + (1) = 10 \to$ Write 0 carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0 0

$6 +3 + (1) = 10 \to$ Write 0 carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0 0 0

$7+2 + (1) = 10 \to$ Write 0 carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0 0 0 0

$6 +3 + (1) = 10 \to$ Write 0 carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0 0 0 0 0

$5 +4 + (1) = 10 \to$ Write 0 carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0 0 0 0 0 0

$4 +5 + (1) = 10 \to$ Write 0 carry 1

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

0 0 0 0 0 0 0

$2 +3 + (1) = 6 \to$ Write 6

2 4 5 6 7 3 8 9

+ 3 5 4 3 2 6 1 1

----------------------------

6 0 0 0 0 0 0 0

Hence:

$24567389+35432611 =6 0 0 0 0 0 0 0$

8 0

3 years ago

What is the solution to 8x - 3(2x - 4) = 3(x - 6)?