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>
Answer:
1 1/7 of a roll of yarn.
Step-by-step explanation:
<h2><u><em>
Brainlest Please!</em></u></h2>
Answer:
7.96 × 10⁸ kg
Step-by-step explanation:
Step 1: Given data
- Mass of the Eiffel Tower (mE): 9.16 × 10⁶ kg
- Mass of the Golden Gate Bridge (mG): 8.05 × 10⁸ kg
Step 2: Determine how many more kilograms is the mass of the Golden Gate Bridge than the mass of the Eiffel Tower
To determine this ratio, we need to do the following subtraction.
mG - mE = 8.05 × 10⁸ kg - 9.16 × 10⁶ kg = 7.96 × 10⁸ kg
The Golden Gate Bridge has approximately 7.96 × 10⁸ kg more than the Eiffel Tower.
Answer: 
Step-by-step explanation:
Given the equation 
, you need find the value of the variable x.
Then, you have to solve for x:
Add 
to both sides of the equation.
Divide by -8 to both sides of the equation.
Once you do this proccedure, you will get the value of the variable x.
Then:
Answer:
probably 4.5
"Step-by-step explanation:
To break even, we need the total profit to be equal to 0. If we make x dollars in 2012, then we need to solve
2.5 + 1.75 + (-3.3) + (-1.4) + x = 0
This gives us x = 0.45 in thousands.
Since the question asks us to give the answer in hundreds, we multiply by 10 and get 4.5. Thus the profit in 2012 must be 4.5 (in hundreds) to break even."
