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

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

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

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

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

Solution steps

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

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

Add a constant to the solution

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

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