how to do antiderivatives?
I can't figure out how to do anti derivatives with a negative exponent. the question is x^-1 +3e^-3x
If you explain how to do that equation too it will be even more helpful. thanks!
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x^(-1) is a special case
If you try to do the antiderivative using the usual power rule then you get x^0/0 which isn't right.
It helps if you know the antiderivative of 1/x is the natural logarithm function, ln x when x>0
When x<0 i guess it's ln (-x) so ln |x| or something , I sort of forget how that part works!
For the other term 3e^(-3 x) the antiderivative is -e^(-3 x) you just divide by the coefficient of x in the exponent. This is actually a change of variable problem but since the exponent is linear you don't have to do it out all the way. If you see e^ k * (some other function of x that's not linear) then you have to do extra work because the derivative comes out of the chain rule for that function up there.
answer ln |x| + C - e^(-3 x).