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...

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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