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elena-s [515]
3 years ago
5

Find integrate (1/(xsqrt(1+(lnx)^2)),1,e,x) ...?

Mathematics
1 answer:
prohojiy [21]3 years ago
4 0
Note that x² + 2x + 3 = x² + x + 3 + x. So your integrand can be written as 

<span>(x² + x + 3 + x)/(x² + x + 3) = 1 + x/(x² + x + 3). </span>

<span>Next, complete the square. </span>

<span>x² + x + 3 = x² + x + 1/4 + 11/4 = (x + 1/2)² + (√(11)/2)² </span>

<span>Also, for the x in the numerator </span>

<span>x = x + 1/2 - 1/2. </span>

<span>So </span>

<span>(x² + 2x + 3)/(x² + x + 3) = 1 + (x + 1/2)/[(x + 1/2)² + (√(11)/2)²] - 1/2/[(x + 1/2)² + (√(11)/2)²]. </span>

<span>Integrate term by term to get </span>

<span>∫ (x² + 2x + 3)/(x² + x + 3) dx = x + (1/2) ln(x² + x + 3) - (1/√(11)) arctan(2(x + 1/2)/√(11)) + C </span>

<span>b) Use the fact that ln(x) = 2 ln√(x). Then put u = √(x), du = 1/[2√(x)] dx. </span>

<span>∫ ln(x)/√(x) dx = 4 ∫ ln u du = 4 u ln(u) - u + C = 4√(x) ln√(x) - √(x) + C </span>

<span>= 2 √(x) ln(x) - √(x) + C. </span>

<span>c) There are different approaches to this. One is to multiply and divide by e^x, then use u = e^x. </span>

<span>∫ 1/(e^(-x) + e^x) dx = ∫ e^x/(1 + e^(2x)) dx = ∫ du/(1 + u²) = arctan(u) + C </span>

<span>= arctan(e^x) + C.</span>
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On average, Shawnee drinks 1/2 of a 6 ounce glass of water in 2/3 hour. How much water does she drink in an hour?
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Answer:

1/2 of 6 = (1/2)*6 = 0.5*6 = 3

Shawnte drinks 3 ounces of water in 2/3 hrs.

3 oz = 2/3 hr

3*(3 oz) = 3*(2/3 hr) .... multiply both sides by 3

9 oz = 2 hrs

She drinks 9 ounces of water in 2 hrs

9/2 oz = 2/2 hrs .... divide both sides by 2

4.5 oz = 1 hr

She drinks 4.5 ounces of water in 1 hour.

6 0
3 years ago
Please help me Arithmetic Reasoning
jek_recluse [69]

Step-by-step explanation:

Price of Jeans = $78.35

30% coupon = 30% × $78.35 = $23.51

6% sales tax = 6% × $78.35 = $4.70

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8 0
3 years ago
1. Use the formula S(d)=√9.8d to calculate the estimated speed, in meters per second, of a tsunami if the disturbance occurred a
postnew [5]

Answer: 1. 210 meters per second .

2.  756  kilometers per hour.

Step-by-step explanation:

Given : The formula S(d)=\sqrt{9.8d} to calculate the estimated speed, in meters per second of a tsunami.

1. If the disturbance occurred at an ocean depth of 4,500 meters.

Then put d= 4500 in the above formula , we get

S(d)=\sqrt{9.8\times4500}

S(d)=\sqrt{44100}=\sqrt{21\times21\times10\times10}\\\\=\sqrt{210^2}=210

Hence, if the disturbance occurred at an ocean depth of 4,500 meters , the estimated speed would be 210 meters per second .

Also, A meter per second is equal to 3.6 kilometers per hour.

i.e. 1 meter per second = 3.6 kilometers per hour

Then by unitary method ,

210 meters per second  =3.6\times210 kilometers per hour

=756  kilometers per hour.

3 0
3 years ago
!*I NEED HELP AND QUICK*!
rewona [7]
1)96/8=12
2)(95*6+5)/6 : (24+1)/3 = (95*6+5)/6 : 2*25/6 = 575/6 *6/50=575/50
=23/2=11 1/2
11 1/2

3) (11 1/2)*12 area of the one  type of the wall, there are 2 such walls
 (11 1/2)*12*2
(8 1/3)*12 area of the second type of the wall, there are 2 such walls
(8 1/3)*12 *2

Altogether area of the walls:
(11 1/2)*12*2 + (8 1/3)*12 *2=12*2(11 1/2 + 8 1/3)= =24(19+3/6+2/6)=24(19+5/6) = 456 +24*(5/6)= 456+20= 476

Tamara needs total 476  square feet, which is less than 480 square feet, so she has enough paint.



5 0
3 years ago
Find the quotient.<br> -72 / -12 =
Shkiper50 [21]

Step-by-step explanation:

it's 6

as,

-12 × 6 = -72

hope this helps you!

4 0
2 years ago
Read 2 more answers
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