piarepm

Answered

2022-01-07

Use partial fractions to find the indefinite integral.

$\int \frac{{x}^{2}+12x+12}{{x}^{3}-4x}dx$

Answer & Explanation

Bob Huerta

Expert

2022-01-08Added 41 answers

Step 1

Given:$I=\int \frac{{x}^{2}+12x+12}{{x}^{3}-4x}dx$

For evaluating given integral, first we simplify given expression then integrate it

Step 2

So,

$I=\int \frac{{x}^{2}+12x+12}{{x}^{3}-4x}dx$

$=\int \frac{{x}^{3}+12x+12}{x({x}^{2}-4)}dx$

$=\int \frac{{x}^{3}+12x+12}{x({x}^{2}-{2}^{2})}dx\text{}\text{}\text{}(\because {a}^{2}-{b}^{2}=(a+b)(a-b))$

$=\int \frac{{x}^{2}+12x+12}{x(x+2)(x-2)}dx$

$=\int (\frac{5}{x-2}-\frac{3}{x}-\frac{1}{x+2})dx\text{}\text{}\text{}(\because \int \frac{dx}{x+a}=\mathrm{ln}|x+a|+c)$

$=5\mathrm{ln}|x-2|-3\mathrm{ln}\left|x\right|-\mathrm{ln}|x+2|+c$

Hence, given integral can be find as above.

Given:

For evaluating given integral, first we simplify given expression then integrate it

Step 2

So,

Hence, given integral can be find as above.

poleglit3

Expert

2022-01-09Added 32 answers

put x=0

put x=2

4+24+12=B2(2+2)

put

karton

Expert

2022-01-11Added 439 answers

Given:

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