Answers
[tex]\large\underline{\sf{Solution-}}[/tex]
Given integral is
[tex]\rm :\longmapsto\:\displaystyle\int\rm \frac{ {x}^{e - 1} + {e}^{x - 1} }{ {x}^{e} + {e}^{x} } \: dx[/tex]
To evaluate this integral, we use Method of Substitution.
So, Substitute
[tex]\rm :\longmapsto\: {x}^{e} + {e}^{x} = y[/tex]
[tex]\rm :\longmapsto\: \dfrac{d}{dx}({x}^{e} + {e}^{x}) = \dfrac{d}{dx}y[/tex]
[tex]\rm :\longmapsto\: {ex}^{e - 1} + {e}^{x} = \dfrac{dy}{dx}[/tex]
[tex]\rm :\longmapsto\:e( {x}^{e - 1} + {e}^{x - 1}) = \dfrac{dy}{dx}[/tex]
[tex]\rm :\longmapsto\:({x}^{e - 1} + {e}^{x - 1})dx = \dfrac{dy}{e}[/tex]
So, on substituting all these values in above integral, we get
[tex]\rm \: = \: \displaystyle\int\rm \frac{dy}{e \: y} [/tex]
[tex]\rm \: = \:\dfrac{1}{e} \displaystyle\int\rm \frac{dy}{ y} [/tex]
[tex]\rm \: = \:\dfrac{1}{e}log |y| + c[/tex]
[tex]\rm \: = \:\dfrac{1}{e}log \bigg| {x}^{e} + {e}^{x} \bigg| + c[/tex]
Hence,
[tex]\rm :\longmapsto\:\boxed{\tt{ \displaystyle\int\rm \frac{ {x}^{e - 1} + {e}^{x - 1} }{ {x}^{e} + {e}^{x} } \: dx = \frac{1}{e}log \bigg| {x}^{e} + {e}^{x}\bigg| + c}}[/tex]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
LEARN MORE :-
[tex]\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf f(x) & \bf \displaystyle \int \rm \:f(x) \: dx\\ \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf k & \sf kx + c \\ \\ \sf sinx & \sf - \: cosx+ c \\ \\ \sf cosx & \sf \: sinx + c\\ \\ \sf {sec}^{2} x & \sf tanx + c\\ \\ \sf {cosec}^{2}x & \sf - cotx+ c \\ \\ \sf secx \: tanx & \sf secx + c\\ \\ \sf cosecx \: cotx& \sf - \: cosecx + c\\ \\ \sf tanx & \sf logsecx + c\\ \\ \sf \dfrac{1}{x} & \sf logx+ c\\ \\ \sf {e}^{x} & \sf {e}^{x} + c\end{array}} \\ \end{gathered}\end{gathered}[/tex]
Related Questions
(Leve
A manufacture manufactures a car for a fixed cost
The car show room determines the selling price to be 55% above the manufacturing
The car show room currently has a sale, reducing all cars be 16%
The sale price of the car is £12,369
Calculate the manufacturing cost of the car.
Answers
Answer:
20068
Step-by-step explanation:
mmm
what time is it in florida im to lazy to look at watch
Answers
2⁴+(2.75+1.75)÷0.9 fast pls helppppp
Answers
Answer:
21
Step-by-step explanation:
First, add the parenthesis
2^4 + 4.50 ÷ 0.9
Second, divide 4.50 by 0.9
2^4 + 5
Third, get rid of the ^4
(2x2x2x2)
16 + 5
21
Pleaseee help me plz
Answers
Answer:
hey there,
hey there,in this question
-7 is multiply by 5 then multiply by-2
-7×5=-35 -35×-2=70i want to inform that when minus is mutiply by minus it become plus
Step-by-step explanation:
hope it help you #BEBRAINLYFind the exterior angle
Answers
Answer:
x = 128 degrees
Step-by-step explanation:
So we know that a triangle's interior angles should add up to 180 degrees.
We also know that when a triangle has that little square in a corner, that corner is equal to 90 degrees.
With these clues, we can figure out that the last interior angle is equal to:
180 - (38+90) = 52, however this isn't the answer we are looking for.
We also know that a straight line is 180 degrees. Therefore, to find the exterior angle we just subtract the interior angle from 180 degrees:
180 - 52 = 128
x = 128
Please help me! Please!
Answers
I think the correlation is negative because the graph is going down.
Hope this helps
What is the remainder R?
Answers
What is remainder R when the polynomial p(x) is divided by (2x - 1)? is (2x - 1) factor of p(x)?
p(x) = 2x² + 3x + 1
Answer :
R = 3
and (2x - 1) not factor of p(x) because, if (2x - 1) factor of p(x) remainder R when the polynomial p(x) divided by (2x - 1) is R = 0
∴ so the answer is option A
Step by step explanation :« Attached »
Please I need help in here :(
Answers
Answer:
5 chairs to 5 tables
5:5
all you have to do is count them and write them in ratio
pls and ty loves!:))))))))))
Answers
Answer:
[tex]f = 9 \div 5c + 32[/tex]
[tex]f - 32 = 9 \div 5c[/tex]
[tex]5(f - 32) = 9c[/tex]
[tex]5(f - 32) \div 9= 9c \div 9[/tex]
Step-by-step explanation:
C = 5(F–32)/9
everything can be found in the solving hope this helps. if you have any worries or doubts don't hesitate to ask me back
Answer:C
Step-by-step explanation:
F=9/5 x C +32
F = -32 =9/5 x C
5/9 (F-32)+C
3 4. What is the slope of the line that passes through (-2, 1) and (8,5)?
Answers
Answer: 2/5
Explanation: Ask if you want an explanation!
The question gives us two points, (-2, 1) and (8,5), from which we can find the slope and later the equation of the line.
Finding the Slope
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= (5 - 1) ÷ (8 - (-2))
= ⁴/₁₀
= ²/₅
Checking my answer:
We can check to see if the answer is correct by drawing the line and seeing if it passes through both points. If it does, then the slope is correct.
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - 1 = ²/₅ (x + 2)
In the graph below (created using Desmos), the line passes through both points. This suggests that we calculated the slope correctly.
A smartphone costs $140. Sales tax is 4%. What is the total cost, including tax?
Answers
Answer:
145.60
Step-by-step explanation:
The ratio of boys to girls in math class is 3 to 5 if there are 9 boys how many girls are there
Answers
Answer:
15
Step-by-step explanation:
for every three boys there are five girls
3 groups of 3 boys
3*5=15 girls
What is 2 1/2 divided by 2 2/3
Answers
Answer:
15/16
Decimal form 0.9375
Step-by-step explanation:
please help I’ll give you a points :,)
use estimation to check whether 96.26 is a reasonable solution fot the equation m-62.74=159
Answers
Answer:
See below
Step-by-step explanation:
I hope you wrote down the right equation using a minus sign instead of a plus.
Rounding 96.26 off to just 96 and then rounding 62.74 off to 62, you can subtract the two in your head real quick.
96 - 62 = 34
So using this estimation you can see that the answer of 159 is no where near correct.
Please help
10x-2-6x=2(2x-1)
Answers
Answer:
All real numbers
Step-by-step explanation:
Given: 10x-2-6x=2(2x-1)
Distribute: 10x-2-6x=4x-2
Simplify like terms: 4x-2=4x-2
Subtract 4x to both sides: -2=-2
Add 2 to both sides: 0=0
All real numbers
Evaluate the expression for the given values of the variables.
5p + 3q for p = 2 and q = −8
When p = 2 and q = −8, the expression is equal to...
Answers
Answer:
[tex] \hookrightarrow \: { \rm{5p + 3q}}[/tex]
p is 2q is -8[tex] = { \tt{5(2) + 3( - 8)}} \\ \\ = { \tt{10 - 24}} \\ \\ = { \underline{ \underline{ \tt{ \: \: - 14 \: \: }}}}[/tex]
gehehehehhehegeheheklelehe
Answers
Answer:
A
Step-by-step explanation:
Please helppppppp :,(
Answers
Answer:
D
Step-by-step explanation:
Please mark brainliest
Please help
Given: P(1, 3)P(1,3)
and
Q(3,7)Q(3,7)
What is the slope of PQPQJ
Answers
Answer:
Slope = 2
Step-by-step explanation:
(1,3) and (3,7)
m = (7-3)/3-1)
= 4/2
= 2
For any of you coding experts. I'm just beginning to take coding seriously and I want to know which coding language is the easiest for beginners. Any tips?
Answers
Answer:
binary codenis the easiest bro it's just 1 and 0 right?
Which of the following shows 24.459 correctly rounded to the hundredths place?
Answers
Answer:
24.46
Step-by-step explanation:
The hundredths place is two places after the decimal. Since the thousandth place is a 9 this would round up the hundredths place to 6.
Pls help me fast!!!!!!!!!!!!
Answers
x=0 I think not 100% sure though
Answer: The equation has infinitely many solutions.
Step-by-step explanation:
With George's end result of 3=3, you can assume that the equation is set up in such a way that no matter what you plug in, you will get the same number on both sides of the equals sign, which means the solution is valid. Therefore this means that there are an infinite number of solutions.
2x/2 = 90/2 pls solve it it
Answers
Answer:
x=45
Step-by-step explanation:
2(45)=90
90/2=90/2
Simplify to create an equivalent expression.
(3n+6)⋅3+(2n+2)⋅4
Please help as soon as possible. Thanks! =D
Answers
Answer:
i don"t know ask your mom
Answer:
[tex](9n + 18) + (8n + 8) \\ = (9n + 8n) + (18 + 8) \\ = 17n + 26[/tex]
What is the equation of the line that passes through the point (-6, -5) and has a slope of -3/2?
Answers
Answer:
y=3/2x+3/2
Step-by-step explanation:
point at (-6,-5)
slope = m = 3/2
y = mx+b
(-6)=(3/2)(-5)+b >>> substituting x & y to solve for b
-6 = (-15/2)+b >>> simplify previous equation
-6 + (15/2) = b >>> isolate and solve for m
3/2 = b
therefore, the equation of the line passing through the point (-6,-5) with a slope of 3/2 is y=(3/2)x+(3/2)
4g+4=2g+12 I need to find what g would equal to
Answers
Answer:
2
Step-by-step explanation:
4g+4=2g+12
or , 4g-2g=12-4
or , 2g = 8
or, g=8/2
g= 2
Answer for brainly please and fast
Answers
Answer:
s = 48
Step-by-step explanation:
A pair of skate blades costs
$189.00. A pair of skate boots
costs 4 times that much. How
much are the skates and blades
all together?
Answers
This is because 4 times the amount of $189 is $756, and $189 + $756 = $945.00
If you do not know please do not answer
A local hamburger shop sold a combined total of 575 hamburgers and cheeseburgers on Sunday. There were 75 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Sunday?
Thanks (*^▽^*)
Answers
What is 1 minus 1 divided by 5
Answers
Answer:
0.8Step-by-step explanation:
Remember PEMDAS
1-1:5=
1-0.2=
0.8