I'm guessing you mean
[tex]\displaystyle \int\frac{x^2+4}{x^2+4x+3}\,\mathrm dx[/tex]
First, compute the quotient:
[tex]\displaystyle \frac{x^2+4}{x^2+4x+3} = 1 + \frac{4x-1}{x^2+4x+3}[/tex]
Split up the remainder term into partial fractions. Notice that
x ² + 4x + 3 = (x + 3) (x + 1)
Then
[tex]\displaystyle \frac{4x-1}{x^2+4x+3} = \frac a{x+3} + \frac b{x+1} \\\\ \implies 4x - 1 = a(x+1) + b(x+3) = (a+b)x + a+3b \\\\ \implies a+b=4 \text{ and }a+3b = -1 \\\\ \implies a=\frac{13}2\text{ and }b=-\frac52[/tex]
So the integral becomes
[tex]\displaystyle \int \left(1 + \frac{13}{2(x+3)} - \frac{5}{2(x+1)}\right) \,\mathrm dx = \boxed{x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C}[/tex]
We can simplify the result somewhat:
[tex]\displaystyle x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C \\\\ = x + \frac12 \left(13\ln|x+3| - 5\ln|x+1|\right) + C \\\\ = x + \frac12 \left(\ln\left|(x+3)^{13}\right| - \ln\left|(x+1)^5\right|\right) + C \\\\ = x + \frac12 \ln\left|\frac{(x+3)^{13}}{(x+1)^5}\right| + C \\\\ = \boxed{x + \ln\sqrt{\left|\frac{(x+3)^{13}}{(x+1)^5}\right|} + C}[/tex]
Which describes the relationship between the distance and the difference?\
Answer:
The distance is always the opposite of the difference.The distance is the absolute value of the difference.
Hope it helps you.Have a nice day!!Answer:
The distance is the absolute value of the difference
Step-by-step explanation:
Sum is the when 2 or more numbers are added . Difference is the quantity at which 2 numbers differ i.e difference between 9 and 7 is 2. If you are talking about distance in reference to segment the distance ishow far apart two points are.
Indicate which is the largest decimal in each of the following pairs.
0.01 and 0.005
Answer:
0.01Step-by-step explanation:
0.01 is the largest decimal in the pair of 0.01 and 0.005
Solve it please with its explaination
Answer:
Answer is 2x^2 + 1x - 15
Step-by-step explanation:
2x^2 + 6x - 5x - 15 2x^2 + 1x - 15
The Torrence family has a rectangular, in-ground pool in their yard. It holds 1700 ft of water. If it is 17 ft wide and 4 ft deep,
what is the length of the pool
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Answer:
25 ft
Step-by-step explanation:
The volume is given by the formula ...
V = LWD . . . . . the product of length, width, depth
Solving for L, we have ...
L = V/(WD) = (1700 ft³)/((17 ft)(4 ft)) = 100/4 ft = 25 ft
The length of the pool is 25 ft.
During a science lab, four-fifths of the class completed the lab and earned a grade of 100. What percent of the class didnt earn a grade of 100?
F. 60%
G. 80%
H. 20%
J.45%
Answer: H. 20%
Step-by-step explanation: if 4/5 got 100 then 80% got 100 so the other 20% did not get a 100
When 2 lines cross, 2 pairs of vertical angles are formed. What is the sum of all 4 angles?
A.
180°
B.
270°
C.
360°
D.
540°
Answer:
C. 360°
Step-by-step explanation:
Two pairs form a complete angle with a sum of 360°.
Please help answering the question
Answer:
I don't know jdjdjdcisveobeobeoxbepxbeoxbwp
which expression represents the phrase below?
8 less than the product of 6 and a number, x
Answer:
6x-8
Step-by-step explanation:
less than means it comes after
product of 6 and a number x
6x
8 less than
6x-8
Algebraic Expressions Use the Distributive Property to expand each expression 4(3x-9)
Answer:
12x-36?
Step-by-step explanation:
well 4×3x and 9× 4 gives the answer
100 yojan=how much km?
Answer:
100 yojan=how much km
1287.48
please brainlist
If a >b, then A must be positive number.
Step-by-step explanation:
NO,IT DEPENDS UPON SITUATIONS
IF B IS -5 THEN A CAN BE -2,-4,-3 OR 1 ,2,3,4,......
your sister is selling girl scout cookies that cost $4.25 a box. your family bought 6 boxes. how many more boxes of cookies must your sister sell in order to $255
Evaluate -1/5 ab if a =3/7 and b =5/8 . Write in simplest form.
Step-by-step explanation:
x = 1/4
4x = 4 * 1/4 = 4/4 = 1.
Which is the graph of f(x) = 100(0.7)?
Answer:
70; The following graph is simply a horizontal line at the value 70.
Step-by-step explanation:
Answer:
Graph A. On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).
Step-by-step explanation:
Edge
Alec wants to purchase a new phone that costs $159.00. His current average net pay is $167.91 each week. What percent of his weekly net pay does Alec need to save each week, for the next six weeks, to reach his goal? Round to the nearest hundredth. (1 point)
1.58%
9.09%
15.78%
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Answer:
15.78%
Step-by-step explanation:
Let x represent the fraction of pay that Alec needs to save each week. Then at the end of 6 weeks, he will have ...
159.00 = 6(x(167.91))
x = 159.00/(6·167.91) ≈ 0.157823 ≈ 15.78%
Alec will need to save 15.78% of his pay.
_____
Additional comment
We recognize that $159 is almost a whole paycheck of $168, so Alec needs to save approximately 1/6 of his paycheck each week. We know that 1/6 = 16.67%, so the nearest reasonable answer choice is 15.78%.
Determine the sum by suitable re arrangement .
a) 6254 + 1297 + 446 + 103 Ans:
b) 1983 + 647 + 217 + 353 2.
Answer:
a.8100
b.3200
Step-by-step explanation:
hope you're okay
Plz solve the following with steps (people who just come by without answering the question and taking the points may end up as ban)
Answer:
12) 3/5=534 students
13) 2151 kg
14)a)7.1 US$
b)total=10.2 US$
Step-by-step explanation:
12)students who had lunch=2/5*890
=356 students
students who did not have lunch=5/5-2/5
=3/5*890
=534 students
14)a)4pens=180 cents
2 books=5.3$
total=7.1 US$
b)5 pens=225 cnets
3 books=7.95 US$
total=10.2 US$
10)ate=1 over 8
remaining=8/8-1/8
=7/8
after six hours=7/8*2/5
=7 over 20
total ate=1/8+7/20
=14+5 over 40
=19 over 40
remaining=40 over 40 - 19 over 40
= 21 over 40
to dog=21/40 *1/4
=21 over 160
total=19 over 40 +21 over 160
=152+21 over 160
=173 over 160
Sorry I am stucked from here.
What is the equation of the line that passes through the point (-5,-7)(−5,−7) and has a slope of \frac{2}{5} 5 2 ?
Answer:
y-y1=slope (x-x1)
where x1=-5, y1=-7 and the slope=2÷5
we substitute for x and y
y-(-7)=2÷5{x-(-5)}
y+7=2÷5(x+5)
y+7=(2x+10)÷5 cross multiply
5y+35=2x+10 collect like terms
5y=2x+10-35
5y=2x-25 ......ans
Points A and B are represented on the number line.
А
B
-ht
-2
-1
0
1
2
Determine whether each inequality is true or false. Choose "True" or "False" for each inequality.
Statement True or False?
IAI > IBI
True
False
IAI > 0
True
False
A>B
True
False
Answer:
Points A and B are represented on the number line.
А
B
-ht
-2
-1
0
1
2
Determine whether each inequality is true or false. Choose "True" or "False" for each inequality.
Statement True or False?
IAI > IBI
False
IAI > 0
False
A>B
true
50% is 20% of what number?
Answer:
I think the answer is 30 percent
Use the distributive property to simplify each expression 10(9-1)
Answer:
see below
Step-by-step explanation:
10(9-1)
Distribute
10 * 9 - 10 *1
90 - 10
80
Answer: 80
Step-by-step explanation:
10(9-1) = 90 - 10 = 80
plz help brainiest to whoever right
Answer:
(1/2)hb = Area of Triangle
s^2 = Area of Square
lw = Area of Rectangle
4s = Perimeter of a Square
2l + 2w = Perimeter of a Rectangle
a + b + c = Perimeter of a Triangle
plz plz help fast plz plZ
no trolls plz
Answer:
3/6 or 1/2
Step-by-step explanation:
3 of the blocks are blue out of 6 blocks. Therefore 3/6.
Evaluate the expression: ab + 2 – 1 Use a = 3 and b = 4
Answer:
[tex]ab + 2 - 1 = ab + 1 \\ a = 3 \\ b = 4 \\ then \: 3 \times 4 + 1 \\ = 12 + 1 = 13 \\ thank \: you[/tex]
2. Which group of numbers is in size order?
A. 3.10 - 3.20 - 3.09 - 3.55
B. 3.09 - 3.10 - 3.2 - 3.5
C. 3.10 - 3.20 - 3.09 - 3.55
D. 3.1 - 3.55 - 3.2 - 3.09
Answer:
B. 3.09-3.10-3.2-3.5 is the answer
Solve for n: n-70=200-(15x4)
I apologize for asking this again but I need help finding the complementary angles, ASAP
Answer:
2nd option is correct
∠AEF and ∠FED , ∠AEG and ∠CEG
Step-by-step explanation:
1st option is a supplementary and even 3rd and 4th options
Help me please!!!٩(๑꒦ິȏ꒦ິ๑)۶
the 1st one
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Explanation:
Add sin(θ)
cos(θ) = sin(θ)
Divide by cos(θ)
1 = sin(θ)/cos(θ) = tan(θ)
Square both sides
1 = tan²(θ)
Add 1
2 = tan²(θ) = sec²(θ)
Take the square root
√2 = sec(θ) . . . . for 0 < θ < π
_____
Additional comment
The equation cos(θ) -sin(θ) = 0 has two solutions: θ = π/4 and θ = 5π/4. For the first-quadrant solution, sec(θ) = √2. For the third-quadrant solution, sec(θ) = -√2.
Please help me solve that question
Step-by-step explanation:
steps are in picture above.
if you need to ask questions I'll give you answers gladly.
9 * (-3/5) ^5
evaluate
pls help :)
Answer:
[tex] - \frac{2187}{3125} [/tex]
Step-by-step explanation:
[tex]9 \times ( \frac{ - 3}{5} )^{5} [/tex]
[tex]( \frac{ - 3}{5} {)}^{5} = \frac{( - 3 {)}^{5} }{ {5}^{5} } [/tex]
[tex] \frac{ - 243}{ {5}^{5} } = - \frac{ 243}{3125} [/tex]
[tex] - 9 \times ( - \frac{243}{3125} )[/tex]
[tex] = - \frac{2187}{3125} [/tex]
