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4 years ago

How do i solve this help asap

Mathematics

1 answer:

shepuryov [24]4 years ago

6 0

9/72

I forgot how to do this

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Whats the intrgral of <img src="https://tex.z-dn.net/?f=%20%5Cint%20%20%5Cfrac%7Bx%5E2%2Bx-3%7D%7B%28x%5E3%2Bx%5E2-4x-4%29%5E2%7

rosijanka [135]

$\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx$

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

$\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx$
$=-\dfrac1{48(x-2)}+\dfrac1{3(x+1)}+\dfrac1{16(x+2)}+\dfrac1{96}\ln|x-2|+\dfrac13\ln|x+1|-\dfrac{11}{32}\ln|x+2|+C$

5 0

4 years ago

You are trying out a new recipe for raisin bread. Each batch of raisin bread dough makes three loaves, and each loaf contains 20

GrogVix [38]

Answer:

0.76 or 76%

Step-by-step explanation:

Please kindly check the attached files for details

8 0

4 years ago

- Keisha has four letter cards that spell out the word MATH. Keisha picks four cards, one at a

zubka84 [21]

Answer:

1/24

Step-by-step explanation:

1/4 x 1/3 x 1/2 x 1/1

1/24

5 0

2 years ago

Line I is a perpendicular bisector

kolezko [41]

Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the Perpendicular Bisector Theorem below.

<h3>What is the perpendicular bisector theorem?</h3>

According to the theorem of perpendicular bisector, any locus on the perpendicular bisector is equidistant from the terminal points of the line segment on which it is created.

Thus, Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the attached image.

Learn more about perpendicular bisectors at:
brainly.com/question/11006922
#SPJ1

4 0

2 years ago

A shoe store advertises that all shoes are on sale for 25% off the regular price. find the sale price of a pair of shoes that ha

DENIUS [597]

100-25=75
find 75% of the 85

percent means parts out of 100
75%=75/100=0.75

'of' means multiply

75% of 85 means
0.75 times 85=63.75

sale price is $63.75

4 0

3 years ago