What is the integral of (12x^{-1}-6x^4-9x^2+5x-15) ?

The integral of (12x^{-1}-6x^4-9x^2+5x-15) is 12ln|x|-(6x^5)/5-3x^3+(5x^2)/2-15x+C

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integral of (12x^{-1}-6x^4-9x^2+5x-15)

\int (12 x^{- 1} - 6 x^{4} - 9 x^{2} + 5 x - 15) d x

12 ln ∣ x ∣ - \frac{6 x ^{5}}{5} - 3 x^{3} + \frac{5 x ^{2}}{2} - 15 x + C

Solution steps

\int 12 x^{- 1} - 6 x^{4} - 9 x^{2} + 5 x - 15 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 12 x^{- 1} d x - \int 6 x^{4} d x - \int 9 x^{2} d x + \int 5 x d x - \int 15 d x

\int 12 x^{- 1} d x = 12 ln ∣ x ∣

\int 6 x^{4} d x = \frac{6 x ^{5}}{5}

\int 9 x^{2} d x = 3 x^{3}

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 15 d x = 15 x

= 12 ln ∣ x ∣ - \frac{6 x ^{5}}{5} - 3 x^{3} + \frac{5 x ^{2}}{2} - 15 x

Add a constant to the solution

= 12 ln ∣ x ∣ - \frac{6 x ^{5}}{5} - 3 x^{3} + \frac{5 x ^{2}}{2} - 15 x + C

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What is the integral of (12x^{-1}-6x^4-9x^2+5x-15) ?
The integral of (12x^{-1}-6x^4-9x^2+5x-15) is 12ln|x|-(6x^5)/5-3x^3+(5x^2)/2-15x+C