Question

find the indefinite integral by u substitution

Answer 1

\[\int\limits 1/(1+\sqrt{2x} )dx\]

Answer 2

I have the solustions manual And amabout to show the part that confuses me.

Answer 3

\[u=1+\sqrt{2x}\]

Answer 4

\[du=1/\sqrt{2x}\]

Answer 5

this much I got on my own, and it agrees with the solutions guide. then they show \[(u-1)du=dx\]

Answer 6

this is where I am confused

Answer 7

where does the (u-1) idea come from?

Answer 8

\[du= \frac {dx}{\sqrt {2x}} \\
\sqrt{2x} du =dx\\
(u-1) du =dx\\


\]
Since
\[ u= 1 +\sqrt{2x}\\
u-1 =\sqrt{2x}
\]

Answer 9

thanks that is exactly what I needed

Answer 10

With pleasure.