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Math Help - Integration Into Arctan

  1. #1
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    Integration Into Arctan





    I couldn't understand this as i have tried using the formula... it leads me to (1/3)*arctan(2z/3) instead of 1/6 in front....

    Please assist. Thank you
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  2. #2
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    Quote Originally Posted by kinkojun View Post




    I couldn't understand this as i have tried using the formula... it leads me to (1/3)*arctan(2z/3) instead of 1/6 in front....

    Please assist. Thank you
    \int \frac{1}{3^2 + (2z)^2} \, dz<br />

    let u = 2z

    du = 2 \, dz

    \frac{1}{2} \int \frac{2}{3^2 + (2z)^2} \, dz

    \frac{1}{2} \int \frac{1}{3^2 + u^2} \, du

    \frac{1}{2} \cdot \frac{1}{3}\arctan\left(\frac{u}{3}\right) + C<br />

    \frac{1}{6}\arctan\left(\frac{2z}{3}\right) + C<br />
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  3. #3
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    Quote Originally Posted by skeeter View Post
    \int \frac{1}{3^2 + (2z)^2} \, dz<br />

    let u = 2z

    du = 2 \, dz

    \frac{1}{2} \int \frac{2}{3^2 + (2z)^2} \, dz

    \frac{1}{2} \int \frac{1}{3^2 + u^2} \, du

    \frac{1}{2} \cdot \frac{1}{3}\arctan\left(\frac{u}{3}\right) + C<br />

    \frac{1}{6}\arctan\left(\frac{2z}{3}\right) + C<br />
    thank you so much!
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