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Fiesta28 [93]
3 years ago
6

Which of the following is the inverse of F(x) if F(x) = 6x?

Mathematics
1 answer:
exis [7]3 years ago
8 0
The best answer is d
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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
Amy buys two shirts. One shirt costs $12.95 and the other costs $15.98. How much money does Amy spend altogether
shtirl [24]

Answer:

$28.93

Step-by-step explanation:

 12.95+15.98 = $28.93

4 0
2 years ago
Read 2 more answers
Find the value of this expression if x = -1 and<br> y = 9.<br> x²y<br> -7
Zarrin [17]

Answer:

-9/7

Step-by-step explanation:

Simplify and remove like terms.

5 0
2 years ago
Brainiest if correct
Mrac [35]
X=14
3 times 14 is 42-13 is 29
3 0
3 years ago
Read 2 more answers
What is angle BCD<br> A. 80°<br> B. 90°<br> C. 100°<br> D. 110°
alexgriva [62]

Answer:

A

Step-by-step explanation:

it is like your hands hold your hand put to make a l shape that is 90⁰ and imaine that more opened out.

7 0
2 years ago
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