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Schach [20]
3 years ago
13

What is the value of for the following data to three decimal places?

Mathematics
1 answer:
Ilya [14]3 years ago
4 0
Answer (B) is you answer
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Integral of x"2+4/x"2+4x+3
dolphi86 [110]

I'm guessing you mean

\displaystyle \int\frac{x^2+4}{x^2+4x+3}\,\mathrm dx

First, compute the quotient:

\displaystyle \frac{x^2+4}{x^2+4x+3} = 1 + \frac{4x-1}{x^2+4x+3}

Split up the remainder term into partial fractions. Notice that

<em>x</em> ² + 4<em>x</em> + 3 = (<em>x</em> + 3) (<em>x</em> + 1)

Then

\displaystyle \frac{4x-1}{x^2+4x+3} = \frac a{x+3} + \frac b{x+1} \\\\ \implies 4x - 1 = a(x+1) + b(x+3) = (a+b)x + a+3b \\\\ \implies a+b=4 \text{ and }a+3b = -1 \\\\ \implies a=\frac{13}2\text{ and }b=-\frac52

So the integral becomes

\displaystyle \int \left(1 + \frac{13}{2(x+3)} - \frac{5}{2(x+1)}\right) \,\mathrm dx = \boxed{x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C}

We can simplify the result somewhat:

\displaystyle x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C \\\\ = x + \frac12 \left(13\ln|x+3| - 5\ln|x+1|\right) + C \\\\ = x + \frac12 \left(\ln\left|(x+3)^{13}\right| - \ln\left|(x+1)^5\right|\right) + C \\\\ = x + \frac12 \ln\left|\frac{(x+3)^{13}}{(x+1)^5}\right| + C \\\\ = \boxed{x + \ln\sqrt{\left|\frac{(x+3)^{13}}{(x+1)^5}\right|} + C}

3 0
2 years ago
Can someone please help?
Fofino [41]
<h2>Your Answer should be:</h2>

<h2>134. </h2><h2></h2>

134

-

120

would equal:

14.

5 0
2 years ago
Read 2 more answers
When you subtract a positive number from a negative number the difference is always
deff fn [24]

The answer is true.

(+)(+)= +

(-)(-)= +

(-)(+)= -

8 0
3 years ago
Macy’s sells 4 TVs for $680. How much would 7 TVs cost?
konstantin123 [22]

First, divide.

680 / 4 = $170 per TV

Second, multiply.

170 * 7 = $1,190

Best of Luck!

5 0
3 years ago
Read 2 more answers
Def is a right triangle if feel equals 24 and de equals 7 find df
makvit [3.9K]

--  If  FE  is the longest side in the right triangle, then
the length of the missing side is  22.956... (rounded).

--  If  FE  is not the longest side in the right triangle,
then the length of the missing side is  25  (exactly).  


5 0
3 years ago
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