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Determine the integral of y=(x+3)/(x^2-9)?
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You need to evaluate the given indefinite integral, hence, you should first reduce the integrand to the most simplified form, such that:
`(x + 3)/(x^2 - 9) = (x + 3)/((x - 3)(x + 3))`
Reducing the duplicate factors, yields:
`(x + 3)/(x^2 - 9) = 1/(x - 3)`
Hence, evaluating the indefinite integral, yields:
`int (x + 3)/(x^2 - 9) dx = int 1/(x - 3) dx`
You should come up with the following substitution, such that:
`x - 3 = t => dx = dt`
Replacing the variable, yields:
`int 1/(x - 3) dx = int 1/t dt`
`int 1/t dt = ln|t| + c`
Replacing back `x - 3` for t yields:
`int 1/(x - 3) dx = ln|x - 3| + c`
Hence, evaluating the given indefinite integral, yields
`int (x + 3)/(x^2 - 9) dx = ln|x - 3| + c` .
Posted by sciencesolve on September 30, 2013 at 4:34 PM (Answer #1)
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