What is the antiderivative of $g(x) = (3 - 6x^3 + 2x^6) / x^6$ ?

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Answer 1 · 2016-05-03T14:15:15

$g(x) = (3 - 6x^3 + 2x^6) / x^6$

$= 3/x^6 - (6x^3)/x^6 + (2x^6) / x^6$

$= 3x^-6 -6x^-3+2$

Use the power rule to find the antiderivative:

$(3x^((-6+1)))/((-6+1)) - (6x^((-3+1)))/((-3+1))+2x/1$

$= (3x^-5)/-5 - (6x^-2)/-2 + 2x$

$= -3/(5x^5) + 6/(2x^2) + 2x$

Get a common denominator to write as a single ratio if you like.

What is the antiderivative of g(x) = (3 - 6x^3 + 2x^6) / x^6g(x) = (3 - 6x^3 + 2x^6) / x^6?