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Math Help - i dont really understand the last step of this inverse trig integration

  1. #1
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    i dont really understand the last step of this inverse trig integration

    i got (integral) 1/(u^2 +7/4) du

    the answer is [2/sq.rt.7]( arctan (2u/sq.rt.7))

    arctan u is the integral of (1/1+u^2)
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  2. #2
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    Quote Originally Posted by twostep08 View Post
    i got (integral) 1/(u^2 +7/4) du

    the answer is [2/sq.rt.7]( arctan (2u/sq.rt.7))

    arctan u is the integral of (1/1+u^2)
    Remember that in general \int\frac{1}{x^2+a^2}dx=\int\frac{dx}{a^2\left(\fr  ac{x^2}{a^2}+1\right)}=\frac{1}{a^2}\int\frac{dx}{  \left(\frac{x}{a}\right)^2+1}

    In this case, your a^2=\frac{7}{4}

    So you're gonna need to use a substitution u=\frac{2x}{\sqrt{7}}.

    EDIT: Sorry I used a different variable. I forgot that you're using u instead of x lol.
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