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

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

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

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

3 e^{\frac{x}{3}} - 2 ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= 3 e^{\frac{x}{3}} - 2 ln ∣ x ∣

Add a constant to the solution

= 3 e^{\frac{x}{3}} - 2 ln ∣ x ∣ + C

\frac{d}{d x} (2^{x} + cos (3 x))

\int \frac{sin ( 2 x )}{47 + cos ^{2} ( x )} d x

y = \frac{6 x}{x ^{2} + 1}, (- 1, - 3)

(3 x)^{^{'}}

\frac{\partial}{\partial x} (y^{2} cos (y))

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