What is the integral of (6x^2+3x+5x^{-1}+3) ?

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

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integral of (6x^2+3x+5x^{-1}+3)

\int (6 x^{2} + 3 x + 5 x^{- 1} + 3) d x

2 x^{3} + \frac{3 x ^{2}}{2} + 5 ln ∣ x ∣ + 3 x + C

Solution steps

\int 6 x^{2} + 3 x + 5 x^{- 1} + 3 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 6 x^{2} d x + \int 3 x d x + \int 5 x^{- 1} d x + \int 3 d x

\int 6 x^{2} d x = 2 x^{3}

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

\int 5 x^{- 1} d x = 5 ln ∣ x ∣

\int 3 d x = 3 x

= 2 x^{3} + \frac{3 x ^{2}}{2} + 5 ln ∣ x ∣ + 3 x

Add a constant to the solution

= 2 x^{3} + \frac{3 x ^{2}}{2} + 5 ln ∣ x ∣ + 3 x + C

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