What is the antiderivative of #3/x^2#?

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Answer 1 · 2016-10-12T22:14:04

#int 3/x^2 dx = -3/x + C#

#3/x^2 = 3x^(-2)#

The power rule of differentiation tells us that:

#d/(dx) x^n = n x^(n-1)#

Hence we find:

#d/(dx) 1/x = d/(dx) x^(-1) = (-1) x^(-2) = -1/x^2#

Hence:

#d/dx (-3/x) = (-3) d/(dx) (1/x) = (-3) (-1/x^2) = 3/x^2#

So:

#int 3/x^2 dx = -3/x + C#