How do you find the antiderivative of #e^-5x# using substitution?

1 Answer
Gió
Feb 3, 2015

I suspect that you want the antiderivative of #e^(-5x)#...
In fact the anti derivative of #e^-5x# is simply: #e^-5x^2/2# (you don't need substitution...#e^-5# is a constant).
However, if you want the antiderivative of #e^(-5x)# you have (if you really want to use substitution):
#inte^(-5x)dx=#
set #-5x=t#
#x=-t/5#
#dx=-dt/5#
So you get:
#inte^t*-dt/5=-1/5e^t+c#
and substituting back:
#=-1/5e^(-5x)+c#

Hope it helps

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