What is the integral of e^{4x}-x^{-1} ?

The integral of e^{4x}-x^{-1} is 1/4 e^{4x}-ln|x|+C

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integral of e^{4x}-x^{-1}

\int e^{4 x} - x^{- 1} d x

\frac{1}{4} e^{4 x} - ln ∣ x ∣ + C

Solution steps

\int e^{4 x} - x^{- 1} 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 e^{4 x} d x - \int x^{- 1} d x

\int e^{4 x} d x = \frac{1}{4} e^{4 x}

\int x^{- 1} d x = ln ∣ x ∣

= \frac{1}{4} e^{4 x} - ln ∣ x ∣

Add a constant to the solution

= \frac{1}{4} e^{4 x} - ln ∣ x ∣ + C

What is the integral of e^{4x}-x^{-1} ?
The integral of e^{4x}-x^{-1} is 1/4 e^{4x}-ln|x|+C