Answer:
thetonwaka
Step-by-step explanation:
I need help please!!!!!
Integrate the following:
[tex]\displaystyle \int \frac{x^2}{x^2+x+3}\, dx[/tex]
Answer:
[tex]\int {\frac{x^2}{x^2+x+3} } \, dx = - \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} ) - \frac{1}{2}ln|x^2+x+3| +x + C[/tex]
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Completing the SquareRearranging VariablesAlgebra II
Long DivisionCalculus
U-Substitution[Integration Trick 1] Numerator Split[Integration Trick 2] Completing the SquareIntegration Rule 1: [tex]\int {cf(x)} \, dx = c\int {f(x)} \, dx[/tex]Integration Rule 2: [tex]\int {f(x)+g(x)} \, dx =\int {f(x)} \, dx + \int {g(x)} \, dx[/tex]Integration 1: [tex]\int {\frac{1}{u} } \, du =ln|u| + C[/tex]Integration 2: [tex]\int {\frac{du}{u^2+a^2} } = \frac{1}{a} arctan(\frac{u}{a} )+C[/tex]Integration 3: [tex]\int {x^n} \, dx = \frac{x^{n+1}}{n+1} +C[/tex]Step-by-step explanation:
Step 1: Define
[tex]\int {\frac{x^2}{x^2+x+3} } \, dx[/tex]
Step 2: Simplify Function
We do long division to simplify the function inside the function.
See Attachment for Long Division Work.
Once we do long division, our function becomes [tex]1-\frac{x+3}{x^2+x+3}[/tex]
Now we rewrite our Integral: [tex]\int ({1-\frac{x+3}{x^2+x+3} }) \, dx[/tex]
Step 3: Integrate Pt. 1
Distributive Integral [Int Rule 1]: [tex]\int {1} \, dx - \int {\frac{x+3}{x^2+x+3} } \, dx[/tex]Integrate 1st Integral [Int 3]: [tex]x - \int {\frac{x+3}{x^2+x+3} } \, dx[/tex]Step 4: Identify Variables Pt.1
Set variables for u-substitution.
u = x² + x + 3
du = (2x + 1)dx
Step 5: Integrate Pt. 2
Rewrite Integral [Int Rule 1]: [tex]x - \frac{1}{2} \int {\frac{2(x+3)}{x^2+x+3} } \, dx[/tex]Distribute 2 [Alg]: [tex]x - \frac{1}{2} \int {\frac{2x+6}{x^2+x+3} } \, dx[/tex]Rewrite Integral [Alg]: [tex]x - \frac{1}{2} \int {\frac{2x+1+5}{x^2+x+3} } \, dx[/tex]Rewrite Integral [Int Trick 1]: [tex]x - \frac{1}{2} [\int {\frac{2x+1}{x^2+x+3} } \, dx + \int {\frac{5}{x^2+x+3} } \, dx ][/tex](2nd Int) Complete the Square: [tex]x - \frac{1}{2} [\int {\frac{2x+1}{x^2+x+3} } \, dx + \int {\frac{5}{(x+\frac{1}{2})^2 + \frac{11}{4} } } \, dx ][/tex]Step 6: Identify Variables Pt. 2
Set variables for u-substitution for 2nd integral.
z = x + 1/2
dz = dx
a = √(11/4)
Step 7: Integrate Pt. 3
[Integrate] U-Substitution: [tex]x - \frac{1}{2} [\int {\frac{1}{u} } \, du + \int {\frac{5}{z^2 + (\sqrt{\frac{11}{4}})^2} } \, dz ][/tex]Rewrite Integral [Int Rule 1]: [tex]x - \frac{1}{2} [\int {\frac{1}{u} } \, du + 5\int {\frac{dz}{z^2 + (\sqrt{\frac{11}{4}})^2} } ][/tex]Integrate 1st Integral [Int 1]: [tex]x - \frac{1}{2} [ln|u| + 5\int {\frac{dz}{z^2 + (\sqrt{\frac{11}{4}})^2} } ][/tex]Integrate 2nd Integral [Int 2]: [tex]x - \frac{1}{2} [ln|u| + 5(\frac{1}{\sqrt{\frac{11}{4}}}arctan(\frac{z}{\sqrt{\frac{11}{4} } } ) ) ][/tex]Distribute 5 [Alg]: [tex]x - \frac{1}{2} [ln|u| + \frac{5}{\sqrt{\frac{11}{4}}}arctan(\frac{z}{\sqrt{\frac{11}{4} } } ) ][/tex]Distribute -1/2 [Alg]: [tex]x - \frac{1}{2}ln|u| - \frac{5}{2\sqrt{\frac{11}{4}}}arctan(\frac{z}{\sqrt{\frac{11}{4} } } )[/tex]Rationalize [Alg]: [tex]x - \frac{1}{2}ln|u| - \frac{5\sqrt{11} }{11}arctan(\frac{z}{\sqrt{\frac{11}{4} } } )[/tex]Resubstitute variables [Alg]: [tex]x - \frac{1}{2}ln|x^2+x+3| - \frac{5\sqrt{11} }{11}arctan(\frac{x+\frac{1}{2} }{\sqrt{\frac{11}{4} } } )[/tex]Simplify/Rationalize [Alg]: [tex]x - \frac{1}{2}ln|x^2+x+3| - \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} )[/tex]Rewrite [Alg]: [tex]- \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} ) - \frac{1}{2}ln|x^2+x+3| +x[/tex]Integration Constant: [tex]- \frac{5\sqrt{11} }{11}arctan(\frac{\sqrt{11}(2x+1) }{11} ) - \frac{1}{2}ln|x^2+x+3| +x + C[/tex]And we have our final answer! Hope this helped you on your Calculus Journey!
hope this will help you........
George places $5,000 into an account that earns a simple interest of 4.3%. John places $5,500 into an account that earns 4%. Who has earned the most interest at the end of 6 years?
Answer/Step-by-step explanation:
George:
4.3% ÷ 100 = 0.043
0.043 × 5000 = 215
John:
4% ÷ 100 = 0.04
0.04 × 5500 = 220
End of 6 years:
George: 215 × 6 = 1290
John: 220 × 6 = 1320
John has earned the most interest at the end of 6yrs. $1320
P decreased by the difference of q and r
Answer:
P-(q-r) that's the answer
Step-by-step explanation:
krnrnenee
Core Algebra
Englis
Solving for an Unknown Using the Distributive Property
180(n-2)
The equation a = represents the angle measuresya, in a regular n-sided polygon. When the equation is
solved for n, n is equal to a fraction with a denominator of a - 180. What is the numerator of the fraction?
Answer:
-360
Step-by-step explanation:
I got it right
5.41 + k = 9.7 what is the value of k
Which of the following functions is graphed below
Answer:
C: y = |x-2| + 3
Step-by-step explanation:
When dealing with transformations, the numbers in the parentheses is the horizontal translation and the numbers outside the parentheses are vertical translation. The only reason the lines are | rather than ( is that they are absolute value.
When taking the horizontal measures, you always flip the sign. So since it is going to the right 2 times, you would think it would be +2, but since it is in the parentheses it would be -2.
When taking the vertical measures, it's just standard thought. So since it is up 3 it would be +3.
Putting all of that together would give you |x-2|+3
need help ASAP mid term .
- 60 points
the metal bar/random line is almost the same size as the other two sides of the triangle. if one side is 32ft, then the opposite side is 32ft also. the bottom is 100ft, so we could eliminate C. because it couldnt be that number. now the bottom triangle, one side is 40ft so the other side has to be 40ft as well. its asking about the metal bar.
its either:
A. 53.2ft or
B. 44.4
because the line is almost the same size as 32ft. its almost a equallateral triangle. i would go with A. though because if you imagine the line at the bottom of the line (100ft.) the line would go over half of it (and 53.2 is over half of 100) so i would say
A.53.2
if this didnt help let me know. and i will delete this (if i can-)
cuánto es 120 por 12
Answer:
120 x 12 = 1440
Step-by-step explanation:
Answer:
es 1440
Step-by-step explanation:
solo pones 120
x12
Laura Simplified the expression 5x[(3.14+4.16)×9+2] as shown
Step 1: 5x[7.3x9+2]
Step 2. 5x[7.3x11]
Step 3. 5x80.3
Step 4. 401.5
Questions:
A. In what step did Laura first make a mistake?
B. Explain what the mistake was using mathematical detail academic language
C. Show your step by step work using mathematical detail and academic language to simplify the expression
D. What is the correct answer to the expression
Answer and Explanation
__________________________________________________________
A. Step 2
B. Step 2 is wrong because multiplying is first before adding, and Laura added before multiplying and got 401.5 instead of 338.5
C. [tex]5\cdot\left(\left(3.14+4.16\right)\cdot9+2\right)[/tex] = [tex]?[/tex]
[tex]5\cdot\left(\left(7.3\right)\cdot9+2\right)[/tex] = [tex]?[/tex]
[tex]5\cdot\left(65.7+2\right)[/tex] = [tex]?[/tex]
[tex]5\cdot\left(67.7\right)[/tex] = [tex]?[/tex]
D. [tex]338.5[/tex]
__________________________________________________________
Hope this helps! <3
__________________________________________________________
What is the circumference of a circular swimming pool with a diameter of 20
feet? (Round your answer to the nearest tenth.)
A. 62.8 ft
B. 15.7 ft
c. 125.7 ft
D. 314 ft
Answer:
A. 62.8 ft
Step-by-step explanation:
[tex]C = \pi \: d = 3.14 \times 20 = 62.8 \: ft[/tex]
Simplify 13 + 4(9 - 7).
A. 34
B. 21
C. 42
D. 19
Answer:
.B. 21
Step-by-step explanation:
13+4(9-7) <----- Multiply 9 and -7 by 4 (Distribute Property)
13+36-28 <----- Combine 36 and -28
13+8 <------Combine 13 and 8
21
Can somebody help please
What is the question?
As more people attend the play, the
amount of money received increases.
Identify the independent variable.
A
people attending
B
money received
Answer:
A
Step-by-step explanation:
Determine the area of the rectangle
6x + 3
X+5
Answer:
Step-by-step explanation:
multiply the two expressions
(6x + 3)(x + 5)
6x^2 + 30x + 3x + 15
6x^2 + 33x + 15
simplify if needed
3(2x^2 + 11x +5)
hope this helps <3
help please I will give brainiest
Find the slope between the points: (3,4) and (-1,-2)
Answer:
3/2 hope this helps hqhahjajja
what is the slope for (-11, 1) and (-2, 6)?
Answer:
5/9
Step-by-step explanation:
You can verify me by using the y2-y1/x2-x1 formula
Ms. Guthrie spent 80% of her cash on gifts.
What fraction of her cash did she spend on gifts?
She spent type your answer...
of her cash on gift.
Answer:
She spend (8/10) or (4/5) of her cash on gift.
Step-by-step explanation:
4/5 is simplified.
but not simplified its 8/10
Explain how you know when 2 ratios are proportional.
Answer:
Ratios are proportional when they represent the same relationship.
Step-by-step explanation:
Such as: finding equivalent fractions
Answer:
Ratios are proportional if they represent the same relationship.
Step-by-step explanation
One good way to tell is to make them fractions and then reduce them. If the reduced fractions are the same, you ratio is proportional! Good luck !
Lin’s family has completed 80% of a trip. They have traveled 40 miles. How far is the trip? *
Answer:
50 miles i believe
Step-by-step explanation:
Answer:
50 miles
Step-by-step explanation:
can yall do the work of the answer 95 to this
9514 1404 393
Answer:
? = 95°
Step-by-step explanation:
Long arc QR is twice the measure of inscribed angle QSR, so is 2×95° = 190°. That, together with the remaining short arcs ? and RS will make up the total circle of 360°.
arc QR + arc RS + ? = 360°
190° +75° +? = 360°
? = 360° -265° . . . . . . subtract 265° from both sides
? = 95°
Which expression is equivalent to 2x^2 - 2x + 7?
Answer:
(o,7) vertical intercept
minimum (1/2 , 13/2)
The box plots below show the miles per gallon (mpg) ratings distribution for three types of cars.
Daniela got 78% on her last history test. If there were 50 questions on the test , how many did she get correct
Answer:
39.
Step-by-step explanation:
78% of 50 is 39. To calculate x% of a number y, we use the following rule: x% of y = (x / 100) × y.
someone please help!! 60 points!!
Answer:
It C am sure it correct....
Answer:
I think the answer would be C.
PLEASE HURRY
In a local city, the temperature at noon is Negative 3 degrees Celsius. The temperature is expected to decrease by 2.5 degrees Celsius each hour until the temperature reaches Negative 18 degrees Celsius. How many hours will it take for the temperature to reach Negative 18 degrees Celsius? 6 hours 7 hours 7.2 hours 8.4 hours
Answer:
6 hours
Step-by-step explanation:
-3-2.5-2.5-2.5-2.5-2.5-2.5=18
srry if I took too long
Answer:
6 HOURS
Step-by-step explanation:
The correct answer would be 6 hours or A!
Hope this helps! Have a great day! :))
Glass melts at a temperature that is higher than 2,500 degrees and less than
3,000 degrees.
Answer:
I think A is correct answer
Answer:
a
Step-by-step explanation:
The points (5, -5) and (9, r) lle
lle on a line with slope - 2. Find the missing coordinate r.
50 points.
Record the simplified expression
Answer:
-4x+5
Step-by-step explanation:
-(4x-2) change sign of each in parenthesis so they are now -4+2
now you have -4x+2+3 add like terms
now you have -4x+5
[tex]\sf \longmapsto−4x+2+3[/tex]
Combine like terms[tex]\sf \longmapsto−4x+2+3[/tex]
[tex]\sf \longmapsto(−4x)+(2+3)[/tex]
[tex]\sf \longmapsto−4x+5[/tex]
