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# Integrate the ∫((r)/(2^(r^2))?

Please intergrate the Indefinite Integral

∫((r)/(2^(r^2))

### 1 Answer

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- gudspelingLv 71 decade agoFavorite Answer
∫((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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