What is the antiderivative of #4x#? thanks!?

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Answer 1 · 2015-06-08T00:55:15

Normally you would use the Power Rule like so to do the derivative:

#d/(dx)[kx^n] = n*kx^(n-1)#
where #k# is a coefficient and #n# is a real number.

With the antiderivative of something on which you can use the power rule to take the derivative, you can do this backwards.

#F(kx^n) = (kx^(n+1))/(n+1)#

So:

#F(4x) = (4x^(1+1))/(1+1) = (4x^2)/2 = 2x^2#

Notice how #d/(dx)[2x^2] = 2*2x^(2-1) = 4x#, so it worked.