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Math Help - integration

  1. #1
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    integration

    how do i intergrate

    sqrt(t^2+t^4)dt?

    thanks!
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  2. #2
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    \displaystyle \sqrt{t^2 + t^4} = \sqrt{t^2(1 + t^2)} = \sqrt{t^2}\sqrt{1 + t^2} = t\sqrt{1 + t^2}.

    So \displaystyle \int{\sqrt{t^2 + t^4}\,dt} = \int{t\sqrt{1 + t^2}\,dt} which you can solve making the substitution \displaystyle u = 1 + t^2.
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  3. #3
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    is it possible to do it by inspection?
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  4. #4
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    Quote Originally Posted by Rine198 View Post
    is it possible to do it by inspection?
    If you can recognise the function that differentiates to give \displaystyle t\sqrt{1 + t^2}, otherwise, just use the substitution...
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