All categories

3 years ago

What is the antiderivative of 3x/((x-1)^2)

Mathematics

1 answer:

ValentinkaMS [17]3 years ago

6 0

Answer:

3 ln(x − 1) − 3/(x − 1) + C

Step-by-step explanation:

∫ 3x / (x − 1)² dx

3 ∫ x / (x − 1)² dx

If u = x − 1, then x = u + 1, and du = dx.

3 ∫ (u + 1) / u² du

3 ∫ (1/u + 1/u²) du

3 (ln u − 1/u + C)

3 ln u − 3/u + C

Substitute back:

3 ln(x − 1) − 3/(x − 1) + C

You might be interested in

A train to New York city leaves a station every 7 minutes. Another train to Boston leaves the station every 6 minutes. Suppose i

Virty [35]

Answer:

7:12 a.m

Step-by-step explanation:

Given that:

Train to New York city leaves station every 7 minutes

Train to Boston leaves station every 6 minutes

Current time = 6:30 a.m

Time both will leave station together is obtained by finding the least common multiple of 6 and 7

Multiples of ;

6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,...

7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70,...

The least common multiple of 6 and 7 is 42.

Hence, both trains will leave the station together after 42 minutes ;

Current time + 42 minutes

6:30 a.m+ 42 minutes = 7:12 a.m

7 0

3 years ago

20 POINTS) Linda has to buy stickers, erasers, and a pencil. She can only spend $3. A sticker costs $0.35, an eraser costs $0.99

jasenka [17]

Answer:

No, because the total will be $3.62

Step-by-step explanation:

When we substitute with 3 and 2 shown below

0.35(3)+0.99(2)+0.59 we get 3.62, which is greater than 3 dollars.

Hope this helped<33

8 0

2 years ago

Read 2 more answers

Which of the following is a ray as shown in the drawing?

OLEGan [10]

Answer:

Step-by-step explanation:

7 0

3 years ago

Could someone help me with this please!

sertanlavr [38]

Angles 1, 3, and 4 make up a straight line.
Thus, 3x + 90 + 3x - 6 = 180 (angle sum of straight line)
6x - 6 = 90
6x = 96

x = 16
Now angle 1 becomes 3(16) = 48
Angle 1, 2, and 3 also make up a straight line.
Thus, angle 2 + 48 + 90 = 180
angle 2 + 138 = 180
angle 2, therefore, becomes 42. In essence, (A)

6 0

3 years ago

Read 2 more answers

Solve for m and n<br> I been stuck on this question for an hour

Crazy boy [7]

Answer:

m = 10 , n = 5 $\sqrt{2}$