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Hitman42 [59]
3 years ago
6

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

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How many three-digit phone prefixes that are used to represent a particular geographic area are possible that have no 0 or 1 in
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The number of possible three-digit phone prefixes that are used to represent a particular geographic area is 640.

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The phone prefixes used to represent a particular geographic area are a 3 digit code consisting of numbers from 0 to 9.

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Condition: The first or the second place cannot take values 0 or 1.

Then the first place can be occupied by the remaining 8 digits.

Similarly the second place can also be occupied by the remaining 8 digits.

And the third place can be occupied by any of the 10 digits.

So the number of ways to construct a phone prefix for any area is:

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