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most general anti-derivative, for g'(x)=(5-4x^3+2x^6)/(x^6)

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dawks | Student, Undergraduate | Honors

Posted December 3, 2011 at 5:47 AM via web

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most general anti-derivative, for g'(x)=(5-4x^3+2x^6)/(x^6)

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted December 3, 2011 at 6:05 AM (Answer #1)

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`g'(x)= (5-4x^3 + 2x^6)/x^6`

`` We need to find the anti derivative g(x).

Then we will find the integral of g'(x).

`==gt g(x)= int g'(x) dx = int (5-4x^3 + 2x^6)/x^6 dx `

`==gt g(x)= int 5/x^6 - (4x^3)/x^6 + (2x^6)/x^6 dx `

`==gt g(x)= int 5x^-6 dx - 4int x^-3 dx+ 2int dx `

`==gt g(x)= (5x^-5)/-5 - 4x^-2/-2 + 2x + C `

`==gt g(x)= -x^-5 + 2x^-2 + 2x + C `

`==gt g(x)= -1/x^5 + 2/x^2 + 2x + C`

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