Find the indefinite integral `int x sqrt((2x-1)) dx` using integration by substitution `int x sqrt((2x-1)) dx` Substitute `u = 2x -1` Gives `x = (u+1)/2` `du = 2x dx` X ( `(du)/(dx) = 2` and `(dx)/(du) = 1/2` )
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`int x sqrt((2x-1)) dx`
`u = 2x - 1` (so `(du)/(dx) = 2` not `2x`)
giving `x = (u+1)/2` ` and (dx)/(du) = 1/2`
Now we have
`int x sqrt((2x-1)) dx =...
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