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Math Help - help plz

  1. #1
    Junior Member
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    help plz

    How would you solve this
    integral of dx/(1+4x^2)
    I know arctan is 1+x^2, but dont see how to solve this to make it look like arctan. thanks.
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  2. #2
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    4x^2 = (2x)^2
    So use the substitution t=2x.
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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     <br />
\begin{aligned}<br />
\int\frac1{1+4x^2}\,dx&=\frac14\int\frac1{\left(\d  frac12\right)^2+x^2}\\&=\frac12\arctan2x+k,\,k\in\  mathbb R<br />
\end{aligned}<br />

    Where \color{red}\int\frac1{a^2+u^2}\,du=\frac1a\arctan\  frac ua+k,\,a\ne0
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  4. #4
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    Quote Originally Posted by Krizalid View Post
     <br />
\begin{aligned}<br />
\int\frac1{1+4x^2}\,dx&=\frac14\int\frac1{\left(\d  frac12\right)^2+x^2}\\&=\frac12\arctan2x+k,\,k\in\  mathbb R<br />
\end{aligned}<br />

    Where \color{red}\int\frac1{a^2+u^2}\,du=\frac1a\arctan\  frac ua+k,\,a\ne0
    Krizalid, it should be |a|.
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