Find an antiderivative G of g(x)=1/x^4
x^(-4) dx
-(1/3) x^-3
or
-1/(3 x^3)
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To find the antiderivative G of g(x) = 1/x^4, we can use the power rule for integration. The power rule states that if g(x) = x^n, where n is any real number except -1, then the antiderivative of g(x) is G(x) = (1/(n+1)) * x^(n+1).
Applying the power rule to g(x) = 1/x^4, we have g(x) = x^(-4) with n = -4. Using the power rule, we get:
G(x) = (1/(-4+1)) * x^(-4+1)
= (1/(-3)) * x^(-3)
= -1/3x^3 + C
Therefore, the antiderivative G of g(x) = 1/x^4 is G(x) = -1/3x^3 + C, where C is the constant of integration.