She can buy 16 cabbages .
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:
Se llama un reemplazo
Step-by-step explanation:
Answer:
The answer is 445,446
Step-by-step explanation:
have a great day everyone :)
<h3>
<u>Answer:</u></h3>

<h3>
<u>Step-by-step explanation:</u></h3>
A figure is given to us in which we can see two triangles one is ∆ MPL and other is ∆MPN .
<u>Figure</u><u> </u><u>:</u><u>-</u><u> </u>



Hence by SAS congruence condition ,
Hence by cpct ( Corresponding parts of congruent triangles ) we can say that , LM = NM = 11 units .
<h3>
<u>Hence </u><u>the</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>LM</u><u> </u><u>is</u><u> </u><u>1</u><u>1</u><u> </u><u>units</u><u> </u><u>.</u></h3>