What is the integral of ((e^x)/3-2/x) ?

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

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integral of ((e^x)/3-2/x)

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

\frac{1}{3} e^{x} - 2 ln ∣ x ∣ + C

Solution steps

\int \frac{e ^{x}}{3} - \frac{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 \frac{e ^{x}}{3} d x - \int \frac{2}{x} d x

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{1}{3} e^{x} - 2 ln ∣ x ∣

Add a constant to the solution

= \frac{1}{3} e^{x} - 2 ln ∣ x ∣ + C

(1 + x)^{- 3}

\int - cos (x) sin (2 x) d x

\int 5 1 - x^{2} d x

\frac{\partial}{\partial x} (3 (x - 1) 2 + 2 (y + 3) 2 + 7)

\int (e^{- 5 x}) d x

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