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Math Help - One more integral substitution

  1. #1
    Senior Member
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    One more integral substitution

    Use a substitution x=f(t) to transform

    integral (0 to 1) x/(x+1) dx into

    integral (0 to infinity) t/((2t+1)*(t+1)^2 dt

    Thanks
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    i'll start with several substitutions:

    1) put x=\frac1u and your integral becomes \int_{1}^{\infty }{\frac{du}{u^{2}(u+1)}}.

    2) put v=u-1 and your integral becomes \int_0^\infty\frac{dv}{(v+1)^2(v+2)}.

    3) put v=\frac1t and your integral becomes \int_0^\infty\frac t{(1+2t)(t+1)^2}\,dt, and we're done.

    you can combine all these substitutions into a single one.
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