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

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

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

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

ln ∣ x ∣ + \frac{1}{3} e^{3 x} + x^{2} + C

Solution steps

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

\int x^{- 1} d x = ln ∣ x ∣

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

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

= ln ∣ x ∣ + \frac{1}{3} e^{3 x} + x^{2}

Add a constant to the solution

= ln ∣ x ∣ + \frac{1}{3} e^{3 x} + x^{2} + C

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