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Bingel [31]
3 years ago
6

Whats the intrgral of

D%20" id="TexFormula1" title=" \int \frac{x^2+x-3}{(x^3+x^2-4x-4)^2} " alt=" \int \frac{x^2+x-3}{(x^3+x^2-4x-4)^2} " align="absmiddle" class="latex-formula">
Mathematics
1 answer:
rosijanka [135]3 years ago
5 0
\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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ANTONII [103]
We can use the Pythagorean theorem to solve this. The Pythagorean theorem is a^2 + b^2 = c^2. We already have a and b, we need to find c. 24^2 + 7^2 is 625. Then, we need to find the square root of 625 to find c. The answer is 25. x = 25.
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3 years ago
Evaluate 24 + |x - 4| - y if x=2 and y= -3<br><br> Help me plz
Sonja [21]

Answer:

\huge  \boxed {29}

Step-by-step explanation:

24 +  |x - 4|  - y

Given x = 2 and y = -3. Therefore, substitute x = 2 and y = -3 in the expression.

24 +  |2 - 4|  - ( - 3) \\ 24 +  | - 2|   + 3

Multiplying the negative with negative equal positive. All negative numbers in the absolute will become positive.

24 + 2 + 3 = 24 + 5 = 29

Therefore the answer is 29.

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3 years ago
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2 years ago
The angles below are supplementary. What is the value of x?
USPshnik [31]
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set the sum of the 2 angles to equal 180 and solve for x

6x + 48 + 60 = 180
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you could check to make sure that your x value is correct by plugging it back into the equation

6(12) + 48 + 60 = 180
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hope this helped!
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Figure out the question
valentina_108 [34]

Answer part A:

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2 years ago
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