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Bingel [31]
3 years ago
6

Whats the intrgral of

D%20" id="TexFormula1" title=" \int \frac{x^2+x-3}{(x^3+x^2-4x-4)^2} " alt=" \int \frac{x^2+x-3}{(x^3+x^2-4x-4)^2} " align="absmiddle" class="latex-formula">
Mathematics
1 answer:
rosijanka [135]3 years ago
5 0
\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx

Notice that x^3+x^2-4x-4=x^2(x+1)-4(x+1)=(x-2)(x+2)(x+1). Decompose the integrand into partial fractions:

\dfrac{x^2+x-3}{(x-2)^2(x+2)^2(x+1)^2}
=\dfrac1{3(x+1)}-\dfrac{11}{32(x+2)}-\dfrac1{3(x+1)^2}-\dfrac1{16(x+2)^2}+\dfrac1{96(x-2)}+\dfrac1{48(x-2)^2}

Integrating term-by-term, you get

\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx
=-\dfrac1{48(x-2)}+\dfrac1{3(x+1)}+\dfrac1{16(x+2)}+\dfrac1{96}\ln|x-2|+\dfrac13\ln|x+1|-\dfrac{11}{32}\ln|x+2|+C
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Need Help with 44.. picture above
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Answer:

Ok:

Step-by-step explanation:

I see that you set up 90 miles = 60 mph * t, where you found out that t = 1.5. What what you needed to do was set 180 miles = 45 mph * t. This is because it is 45 mph for the <em>whole</em> trip. Then, you find that t = 4 hours. That that means that he spent 2.5 hours driving back. Then, we can do d=vt and find 90/2.5 as the speed he went home at. Which comes out to be 36 mph.

8 0
3 years ago
Eddie walks 450.25 feet in 2.5 minutes. Which value is closest to the number of yards Eddie walks in 1 minute?
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Eddie walks 60.03 yards in 1 minute using proportion.

What is proportion?

The term proportionality refers to any relationship that has the same ratio every time. The proportional relationship between the two supplied ratios is defined by an equation. In other terms, the proportion declares that the two fractions or ratios are equal. For instance, the average number of apples per tree determines the proportionality between the quantity of apples in a crop and the number of trees in the orchard.

Here let us take time and distance as proportional values,

=> \frac{distance}{Time}

=> 450.25/2.5 = x/1

=> x = 180.1 feet.

To convert feet to yards divide the length by 3. then

=> 180.1/3=60.03 yards,

Therefore Eddie Walks 60.03 yards in 1 minute.

To learn more about proportion refer the below link

brainly.com/question/19994681

#SPJ1

7 0
11 months ago
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