Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

Integrate the ∫((r)/(2^(r^2))?

Please intergrate the Indefinite Integral

∫((r)/(2^(r^2))

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  • 1 decade ago
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    ∫((r)/(2^(r^2)) dr

    Let u=r^2

    du = 2rdr

    The integral simplifies to

    ∫1/(2^u)du

    = ∫2^(-u) du

    Now 2^x = e^(x.ln2)

    Therefore 2^(-u) = e^(-uln2)

    ∫2^(-u) du

    = ∫e^(-u.ln2) du

    = -[1/(ln(2)]e^(-u(ln2))] + c

    But u = r^2

    Integral = -[1/(ln(2)]e^(-(r^2)(ln2))] + c

    = -[1/ln(2)][1/2^(r^2)] + c

    = -1/[(2^(r^2))* ln(2)] + c

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