What is the antiderivative of #f'(x)=2x-3/x^4#?

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Answer 1 · 2018-04-10T22:00:35

#f(x)=x^2+1/x^3+C#

Rewrite with negative exponents to make things easier to visualize.

#f'(x)=2x-3x^(-4)#

Recall the antiderivative of a term #x^a# raised to a power #a# is given by

#x^(a+1)/(a+1)+C, a!=-1#, #C# is an arbitrary constant

So,

#f(x)=2x^(1+1)/(1+1)-3x^(-4+1)/(-4+1)+C#

Simplify.

#f(x)=x^2+x^-3+C#

#f(x)=x^2+1/x^3+C#