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

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

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

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

x^{3} + ln ∣ x ∣ + C

Solution steps

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

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= \int 3 x^{2} + \frac{1}{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 3 x^{2} d x + \int \frac{1}{x} d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

= x^{3} + ln ∣ x ∣

Add a constant to the solution

= x^{3} + ln ∣ x ∣ + C

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