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goldenfox [79]
2 years ago
5

Beinggreat78 your lookin for this lol

Mathematics
1 answer:
nadya68 [22]2 years ago
8 0
Step-by-step explanation below

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The following integral requires a preliminary step such as long division or a change of variables before using the method of par
shtirl [24]

Division yields

\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}

Now for partial fractions: you're looking for constants <em>a</em>, <em>b</em>, and <em>c</em> such that

\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}

\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a

which gives <em>a</em> + <em>b</em> = 2, <em>c</em> = 0, and 2<em>a</em> = -7, so that <em>a</em> = -7/2 and <em>b</em> = 11/2. Then

\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}

Now, in the integral we get

\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx

The first two terms are trivial to integrate. For the third, substitute <em>y</em> = <em>x</em> ² + 2 and d<em>y</em> = 2<em>x</em> d<em>x</em> to get

\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}

7 0
2 years ago
Use the reverse tabular method to solve division problem: (x^4+2x^3+2x^2+2x+1)/(x+1)
svetoff [14.1K]

Answer:

x^3 +x^2 +x+1

Step-by-step explanation:

Your welcome!!!!!!!!!!!

3 0
3 years ago
If you wanted to know the difference between the highest paid employee and the lowest paid employee, would you look at the mean,
katovenus [111]
You would use mean.



5 0
3 years ago
Todd bought g boxes of granola bars. There are 12 granola bars in each box. Write an expression that shows how many granola bars
mr_godi [17]

Answer:

Total bars = 12g

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Need help pls pls pls pls pls pls
Crazy boy [7]

Answer:

d.

Step-by-step explanation:

hi I think its d, sorry if I'm wrong

6 0
3 years ago
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