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3 years ago

5

Integrate ln(x^2-x+2).

1 answer:

Lilit [14]3 years ago

4 0

∫㏑(x² - x + 2) dx = ∫㏑(x² - 2x + x + 2) dx
∫㏑(x² - x + 2) dx = ∫㏑[x(x) - x(2) + 1(x) - 1(2)] dx
∫㏑(x² - x + 2) dx = ∫㏑[x(x - 2) + 1(x - 2)] dx
∫㏑(x² - x + 2) dx = ∫㏑[(x + 1)(x - 2)] dx
∫㏑(x² - x + 2) dx = ∫㏑(x + 1) + ㏑(x - 2) dx
∫㏑(x² - x + 2) dx = ∫㏑(x + 1) dx + ∫㏑(x - 2) dx
∫㏑(x² - x + 2) dx = [x㏑(x + 1) - (x - ㏑(|x + 1|)) + C] + [x㏑(x - 2) - (x + ㏑(|x - 2|)) + C]
∫㏑(x² - x + 2) dx = [x ln(x + 1) + x㏑(x - 2)] + [(-x +㏑(|x + 1|)) + (-x - ln(|x - 2))] + {C + C}
∫㏑(x² - x + 2) dx = x㏑(x² - x + 2) + [-2x - (㏑(|x + 1|))/㏑(|x - 2|))] + 2C
∫㏑(x² - x + 2) dx = x㏑(x² - x + 2) - 2x - (㏑(|x + 1|))/㏑(|x - 2|)) + 2C

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nataly862011 [7]

Ley pt S have coordinates (x,y)
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3 years ago

A man walks for x hours at a speed of

alexandr1967 [171]

Given:

A man walks for x hours at a speed of (x + 1) km/h and cycles for (x - 1) hours at a speed of (2x + 5) km/h.

Total distance travelled is 90 km.

To find:

The value of x.

Solution:

We know that,

$Speed=\dfrac{Distance}{Time}$

$Speed\times Time=Distance$

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The man cycles for (x - 1) hours at a speed of (2x + 5) km/h, so the cycling distance is

$D_2=(2x+5)(x-1)$ km

Now,

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$(x+1)x+(2x+5)(x-1)=90$

$x^2+x+2x^2-2x+5x-5-90=0$

$3x^2+4x-95=0$

$3x^2+19x-15x-95=0$

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$3x+19=0\text{ and }x-5=0$

$x=\dfrac{-19}{3}\text{ and }x=5$

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2 years ago

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Answer:

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Step-by-step explanation:

so first the equation for the situation has been given which is

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now you can just solve since it's a linear equation

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take 16 to the other side to get

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solve to get x (adult price)

which is 84

remember the. child's price is 8 less

84-8=76

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iVinArrow [24]

Answer:

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