- #1
3ephemeralwnd
- 27
- 0
Ive just started learning about integration and antiderivatives in class, and I've got a question
Say we have:
f(x) = 1/x^3 , and f'(x) = F(x)
g(x) = 1/X , and g'(x) = G(x)
then to find the antiderivative of f(x), i would solve it like this:
first rewrite it as : x^(-3),
= x^(-3 + 1) / ( -3+1)
= x^ (-2) / (-2)
which i believe is the correct antiderivative function
but for g(x), if i were to use the same method, i'd get
x^(-1),
= x^(-1+1)
= x^0
= 1
but the actual antiderivative is ln|x| (since the derivative of lnx = 1/x)
why doesn't that the first method work anymore?
Say we have:
f(x) = 1/x^3 , and f'(x) = F(x)
g(x) = 1/X , and g'(x) = G(x)
then to find the antiderivative of f(x), i would solve it like this:
first rewrite it as : x^(-3),
= x^(-3 + 1) / ( -3+1)
= x^ (-2) / (-2)
which i believe is the correct antiderivative function
but for g(x), if i were to use the same method, i'd get
x^(-1),
= x^(-1+1)
= x^0
= 1
but the actual antiderivative is ln|x| (since the derivative of lnx = 1/x)
why doesn't that the first method work anymore?