∫_(-∞)^0▒〖x5^(-x^2 ) dx〗
the definite integral is form -infinite to zero. this problem involves some of L'hopital
the definite integral is form -infinite to zero. this problem involves some of L'hopital
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∫x*5^(-x^2) dx from -inf to 0
u = -x^2
du/-2 = x dx
-1/2*∫5^(u) du from -inf to 0
-1/2*5^(u)/ln(5) eval. from -inf to 0
= -1/(2*ln(5)) + lim a-> -inf 1/2*5^(u)/ln(5) = -1/(2*ln(5)) + 0 = -1/(2*ln(5))
u = -x^2
du/-2 = x dx
-1/2*∫5^(u) du from -inf to 0
-1/2*5^(u)/ln(5) eval. from -inf to 0
= -1/(2*ln(5)) + lim a-> -inf 1/2*5^(u)/ln(5) = -1/(2*ln(5)) + 0 = -1/(2*ln(5))