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How solve integral 1/x(ln x+2)^4 ?
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You need to evaluate the following indefinite integral, such that:
`int 1/(x(ln x+2)^4)dx`
You should come up with the following substitution, such that:
`ln x + 2 = t => 1/x dx = dt`
Replacing the variable, yields:
`int (dt)/t^4 = int t^(-4)dt`
`int t^(-4)dt = t^(-4+1)/(-4+1) + c`
Replacing back `ln x + 2` for t yields:
`int 1/(x(ln x+2)^4)dx = -1/(3(ln x + 2)^3) + c`
Hence, evaluating the indefinite integral, using substitution, yields `int 1/(x(ln x+2)^4)dx = -1/(3(ln x + 2)^3) + c.`
Posted by sciencesolve on July 3, 2013 at 2:36 PM (Answer #1)
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