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:
x=-2
Step-by-step explanation:
5x -10x- 30= 10x
-5x -30 = 10x
-30=15x
x=-2
The answer to this question is 1,193,400,00 ml of gasoline. We can reach this conflusion through the following equation:
3.9
x 10^3 10 x 10 x 103.9 x 1,0003,900 ml per second. Then, to work out
how many ml are burned in a minute, multiply 3,900 by 60. Therefore, we
can establish that ne commercial airplane burns around 234,000 ml of
gasoline per minute. Next, consider the equation 5.1 x 10^35.1 x 10 x 10
x 105.1 x 1,0005,100. From this, we can work out that 5,100 airplanes
burn 1,193,400,000 ml of gasoline in one minute.
Answer:
$5.50 per hour
Step-by-step explanation:
44 divided by 8 equals 5.5
<span>Jason had ¾ pound of Salami.
He used 1/3 of it for sandwhich, now find the number of pound of salami left.
=> ¾ - 1/3
=> ¾ - 1/3, since the given equation contains different denomination, find
the least common denominator
=> so the LCD is 12
=> ¾ - 1/3 = 9/12 – 4/12
=> 9/12 – 4/12
=> 5/12
Thus, the answer is letter C. 5/12 pounds is left to Jason’s Salami.</span>
