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2 years ago

Please help and explain how you got the answer. Im giving out brainliest. || Q4

Mathematics

2 answers:

alexdok [17]2 years ago

8 0

Answer:

Step-by-step explanation:

Inside the parentheses, we see 5+3, which equals 8. Now, do 8x4, which equals 32!

rosijanka [135]2 years ago

4 0

Answer: 32

Step-by-step explanation:

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Answer:

Step-by-step explanation:

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Following PEMDAS, you would begin with solving within the ( ). So being that m = 8 you plug that in. Then subtract 6 from 8 which would then give you 2. The multiply 7 by 2, which gives you 14.

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Karo-lina-s [1.5K]

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2 years ago

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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

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

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