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Integrate `int 1/(5 - 4x) dx`
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Use substitution to transform the above integral iinto an easier to handle integral.
You should come up with the following substitution: 5-4x = u.
Differentiating the equation `5-4x = u` yields: `-4dx = du =gt dx = -du/4`
Write the new integral:
`int (-du/4)/(u) = (-1/4)*int (du)/u`
Notice that this integral is easier to handle.
`(-1/4)*int (du)/u = (-1/4)*ln |u| + c`
Replacing u by 5-4x yields:
`int dx/(5-4x) = (-1/4)*ln |5-4x| + c`
Evaluating the integal yields:`int dx/(5-4x) = (-1/4)*ln |5-4x| + c.`
Posted by sciencesolve on December 6, 2011 at 11:21 PM (Answer #1)
The integral to be evaluated is`int 1/(5-4x) dx`
Let y = 5 - 4x
`dy/dx = -4`
`dx = dy/(-4)`
Substituting the above in the original integral:
`int 1/(5 - 4x) dx`
=> `int (1/y)(1/-4)dy`
=> `(-1/4) int (1/y) dy`
=> `-(ln y)/4`
substitute y = 5 - 4x
=> `-ln(5-4x)/4 + C`
=> `-ln(5-4x)^(1/4) +C`
=> `ln(1/(5-4x)^(1/4)) + C`
The required integral is `ln(1/(5 - 4x)^(1/4)) + C`
Posted by justaguide on December 8, 2011 at 6:32 PM (Answer #2)
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