(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\int \frac{1}{1+\sqrt{2x}}dx[/tex]

2. Relevant Equations

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

[tex]\sqrt{2x}=u-1[/tex]

[tex]dx=(u-1)du[/tex]

3. The attempt at a solution

I was able to get it down to:

[tex]\int (1-\frac{1}{u})du[/tex]

[tex]= u-\ln{lul}}+C[/tex]

[tex]= 1+\sqrt{2x}-\ln{l1+\sqrt{2x}l}+C[/tex]

However, my book says that the solution to the integral is:

[tex] \sqrt{2x}-\ln{l{1+\sqrt{2x}l}+C[/tex] (Without the 1 in front)

Why is this? Thanks in advance for your help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integration by u- substitution (involving natural logs)

**Physics Forums | Science Articles, Homework Help, Discussion**