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Murljashka [212]
3 years ago
5

7/3x+1/3x=1+5/3xplz help ​

Mathematics
1 answer:
liubo4ka [24]3 years ago
7 0
(Multiply all by 3 )
7x+x=3+5x
8x=3+5x
3x=3
x=1
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This is a question on my partial fractions homework, but no matter what I try I can't figure it out..
Ierofanga [76]
\dfrac{x^2+x+1}{(x+1)^2(x+2)}=\dfrac{a_1x+a_0}{(x+1)^2}+\dfrac b{x+2}
\implies\dfrac{x^2+x+1}{(x+1)^2(x+2)}=\dfrac{(a_1x+a_0)(x+2)+b(x+1)^2}{(x+1)^2(x+2)}
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So you have

\displaystyle\int_0^2\frac{x^2+x+1}{(x+1)^2(x+2)}\,\mathrm dx=-2\int_0^2\frac x{(x+1)^2}\,\mathrm dx-\int_0^2\frac{\mathrm dx}{(x+1)^2}+3\int_0^2\frac{\mathrm dx}{x+2}
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where in the first integral we substitute x\mapsto x+1.

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=\dfrac23+\ln\dfrac89
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Answer:

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