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Math Help - Integration of product

  1. #1
    Senior Member I-Think's Avatar
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    Integration of product

    How do I integrate \int{x\sqrt{4x^2+1}}

    I've tried parts with x=dv and \sqrt{4x^2+1}=u and vice-versa and I still don't get the answer. Help please.

    N.B. When hinting at the answer, note that I cannot use hyperbolic trig functions, it's off the syllabus.
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  2. #2
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    Quote Originally Posted by I-Think View Post
    How do I integrate \int{x\sqrt{4x^2+1}}
    This is \int {\frac{{\sqrt u du}}{8}}
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  3. #3
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    Quote Originally Posted by I-Think View Post
    How do I integrate \int{x\sqrt{4x^2+1}}

    I've tried parts with x=dv and \sqrt{4x^2+1}=u and vice-versa and I still don't get the answer. Help please.

    N.B. When hinting at the answer, note that I cannot use hyperbolic trig functions, it's off the syllabus.
    You don't need to use integration by parts here. Consider the substitution u = 4x^2 which gives dx = \frac{du}{8x}

    It should be apparent now what to do.
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