SOLVED:Use partial fractions to find the integral. ∫(5 x^2-12 x-12)/(x^3-4 x) d x

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Ron Larson, Bruce Edwards

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Chapter 8, Problem 12

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Use partial fractions to find the integral.$\int \frac{5 x^{2}-12 x-12}{x^{3}-4 x} d x$

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Official textbook answer

Video by Darshan Maheshwari

Numerade Educator

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02:16

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\int \frac{5-x}{2 x^{2}+x-1} d x
$$
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Use partial fractions to find the indefinite integral.
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Use partial fractions to find the indefinite integral.
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\int \frac{x^{2}+12 x+12}{x^{3}-4 x} d x
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Transcript

well, we need to find the partial fraction off this, and then we need to integrate that. So let’s first. The first thing is we will factories the denominator completely. So the numerator remains as it is. We have the denominator as X has taken out, we’re left with X squared minus four. From here, this can better denies further becomes this can X squared minus four can better than us X Square minus two a square so that that is the difference. The difference of the perfect square the numerator remains as it does. The denominator becomes X plus two and times explains to in D X. Now we have fact razor denominator completely. So let’s do the partial fractions. So this becomes X X plus two X managed to since all the factors are linear, so we’ll write the partial fraction in the form of a war. X must be over expressed to a C over X minus two. Over here, we’ll replace the street battle. Been simplified this full father become five X squared minus 12 x minus 12. This will be equal toe eight times, expressed two times X minus two plus B times X time six months to plus C times, X Times Express to and how we got this we have multiplied, Uh, the second this is expressed to So let’s try this express to a little bit. Who was her denominator so? Or to the left Next line, in fact, So how we got this? We were deployed both sides by X X plus two x men’s, too. Now, in order to find the values of A, B and C, the first thing which we do is we substitute X as zero. So when you protect zero here we get minus 12. This…

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