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

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

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

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

\frac{5 x ^{2}}{2} + 3 ln ∣ x ∣ + C

Solution steps

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

3 x^{- 1} = \frac{3}{x}

= \int 5 x + \frac{3}{x} 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 5 x d x + \int \frac{3}{x} d x

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{5 x ^{2}}{2} + 3 ln ∣ x ∣

Add a constant to the solution

= \frac{5 x ^{2}}{2} + 3 ln ∣ x ∣ + C

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