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Math Help - Integration

  1. #1
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    Integration

     \int t^2 (1+t^2)^\frac {1}{2}dt

    How can I do this?

    If I use a substitution,
    u=1+t^2 => t = (u-1)^1/2

    then du/dt = 2t

    Then it is more complex. What to do?
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  2. #2
    Member Danshader's Avatar
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    try using u = tan x
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  3. #3
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    Quote Originally Posted by Danshader View Post
    try using u = tan x
    Ya. I get it. Thanks
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by geton View Post
     \int t^2 (1+t^2)^\frac {1}{2}dt

    How can I do this?

    If I use a substitution,
    u=1+t^2 => t = (u-1)^1/2

    then du/dt = 2t

    Then it is more complex. What to do?
    This is actually a very difficult integral...Deshand was right you cant use algaebraic substitution to a happy end
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  5. #5
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by geton View Post
     \int t^2 (1+t^2)^\frac {1}{2}dt

    How can I do this?

    If I use a substitution,
    u=1+t^2 => t = (u-1)^1/2

    then du/dt = 2t

    Then it is more complex. What to do?
    With trig sub you hget \int\tan^2(\theta)\sec(\theta)d\theta
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