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Integrate the following functions x/e^(x...

Integrate the following functions `x/e^(x^2)`

Text Solution

Verified by Experts

Let `x^2 = t. Then
dt = 2x dx `gt xdx = (dt)/2`
therefore` int x/e^(x^2) dx = int x e^(-x^2) dx`
=`int e^(-1) (dt)/2 = 1/2 xx e^(-1)/(-1) +c`
=`-1/2 e^(-1)+c = -1/2 e^(-x^2) +c`
=`-1/(2e^(x^2) +c`
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