Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Trigonometric substitution

  1. Mar 23, 2010 #1

    [tex]
    \int\frac{x}{\sqrt{x^2+x+1}}dx
    [/tex]
    [tex]
    \int \frac{x}{\sqrt{(x+\frac{1}{2})^2+\frac{3}{4}}}dx
    [/tex]
    [tex]
    u=x+\frac{1}{2}
    [/tex]
    [tex]
    \int \frac{u-\frac{1}{2}}{\sqrt{u^2+\frac{3}{4}}}du
    [/tex]
    [tex]
    u=\frac{\sqrt{3}}{2}tanT
    [/tex]
    [tex]
    du=\frac{\sqrt{3}}{2}sec^2TdT
    [/tex]
    [tex]
    \int \frac{\frac{(\sqrt{3}}{2}tanT-\frac{1}{2})\frac{\sqrt{3}}{2}sec^2T}{\frac{\sqrt{3}}{2}secT}dT
    [/tex]
    [tex]
    \int (\frac{\sqrt{3}}{2}tanT-\frac{1}{2})secTdT
    [/tex]
    [tex]
    \frac{\sqrt{3}}{2}secT-\frac{1}{2}ln|secT+tanT|+C
    [/tex]
    [tex]
    \frac{\sqrt{u^2+\frac{3}{4}}}{2}-\frac{ln|\sqrt{u^2+\frac{3}{4}}+2u|}{2}+C
    [/tex]
    [tex]
    \frac{\sqrt{x^2+x+1}}{2}-\frac{ln|\sqrt{x^2+x+1}-2x+1|}{2}
    [/tex]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted