$\frac{x-1}{x^2+3x+2}\\\frac{x-1}{(x+1)(x+2)}\\\frac{x-1}{(x+1)(x+2)}=\frac{A}{x+2}+\frac{B}{x+1}\\x-1=A(x+1)+B(x+2)\\\\\text{ Let } x=-1 \text{ then } -2=A(0)+B(-1+2) \text{ which means } B=-2\\\\\text{ Instead of choose } x \text{ to be -1, let's now set it equal to -2 to find } A\\\\-3=A(-1)+B(-2+2)\\-3=-A\\A=3\\\\ \text{ So your integral becomes } \\\int \frac{3}{x+2} dx+\int \frac{-2}{x+1} dx\\3 \ln|x+2|-2\ln|x+1|+C\\\\or\\-2\ln|x+1|+3\ln|x+2|+C$

8 0

3 years ago

A regular pentagon is shown. A regular pentagon has side lengths of 9.4 centimeters and a radius of 8 centimeters. What is the l

Angelina_Jolie [31]

Answer:

6.5 cm

Step-by-step explanation:

The computation of the length of the apothem is shown below:

Given that

The side length is 9.4 centimeters

And, the radius is 8 centimeters

Now based on the above information

As per the attached figure

AB = 8 cm

BC = 9.4 ÷ 2 = 4.7 cm

Now apply the pythagoras theorem

AB^2 = BC^2 + AC^2

8^2 = 4.7^2 + AC^2

AC^2 = 41.91

AC = 6.47 cm

= 6.5 cm

7 0

3 years ago

PLEASE HELP!!!!!!!!!!!!

bixtya [17]

Answer: Numbers of servings: 10 and 13, Liters of punch: 14

Step-by-step explanation:

Number of servings - 6 = Liters of punch.

4 0

2 years ago

On Monday, a bakery sold 67 dozen cookies. How many total cookies did the bakery sell?

gulaghasi [49]

Answer:

804

Step-by-step explanation:

dozen means 12

67 times 12 is 804

8 0

1 year ago

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