Please help me with this definite integral
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Please help me with this definite integral

[From: ] [author: ] [Date: 11-10-30] [Hit: ]
......
∫_(-∞)^0▒〖x5^(-x^2 ) dx〗

the definite integral is form -infinite to zero. this problem involves some of L'hopital

-
∫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))
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