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

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

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

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

2 ln ∣ x ∣ + x^{3} + C

Solution steps

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

2 x^{- 1} = \frac{2}{x}

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= 2 ln ∣ x ∣ + x^{3}

Add a constant to the solution

= 2 ln ∣ x ∣ + x^{3} + C

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\int \frac{1}{t} cos (t + 3) d t

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