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Math Help - Intergration Problem - Square Roots?

  1. #1
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    Intergration Problem - Square Roots?

    \frac{3}{\sqrt{2t +1}}

    Can someone please explain how I do this. The square root on the bottom has really thrown me out. I can do them when there's no square root but because it's there I'm really not sure.

    I was thinking,

    \frac{3}{2} (2t+1)^{1/2}

    but yeah I'm not really sure.

    Thanks!
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Kaynight View Post
    \frac{3}{\sqrt{2t +1}}

    Can someone please explain how I do this. The square root on the bottom has really thrown me out. I can do them when there's no square root but because it's there I'm really not sure.

    I was thinking,

    \frac{3}{2} (2t+1)^{1/2}

    but yeah I'm not really sure.

    Thanks!
    Let

    \varphi=2t+1\Rightarrow{dt=\frac{1}{2}\varphi}

    So we have

    \frac{3}{2}\int\frac{d\varphi}{\sqrt{\varphi}}=3\s  qrt{\varphi}

    Now back subbing we get

    3\sqrt{2t+1}
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  3. #3
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    Isomorphism's Avatar
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    Quote Originally Posted by Kaynight View Post
    \frac{3}{\sqrt{2t +1}}

    Can someone please explain how I do this. The square root on the bottom has really thrown me out. I can do them when there's no square root but because it's there I'm really not sure.

    I was thinking,

    \frac{3}{2} (2t+1)^{1/2}

    but yeah I'm not really sure.

    Thanks!
    Wrong, substitute u = 2t+1, 3\int (2t+1)^{-\frac12}\, dt = 3 \int u^{-\frac12} \, \frac{du}2 = \frac32 \int u^{-\frac12} \, du = 3\sqrt{2t+1}
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  4. #4
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    Many thanks Isomorphism and Mathstud28!
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