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 =...

$\displaystyle\int{x}$
sqrt((2x-1)) dx

$\displaystyle{u}={2}{x}-{1}$ (so $\displaystyle\frac{{{d}{u}}}{{{\left.{d}{x}\right.}}}={2}$ not $\displaystyle{2}{x}$ )

giving $\displaystyle{x}=\frac{{{u}+{1}}}{{2}}$ $\displaystyle{\quad\text{and}\quad}\frac{{{\left.{d}{x}\right.}}}{{{d}{u}}}=\frac{{1}}{{2}}$

Now we have

$\displaystyle\int{x}\sqrt{{{\left({2}{x}-{1}\right)}}}{\left.{d}{x}\right.}=\ldots$

Spooky Notes