What is the integral of (e^x+(14)/x-3/(x^2)) ?

The integral of (e^x+(14)/x-3/(x^2)) is e^x+14ln|x|+3/x+C

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integral of (e^x+(14)/x-3/(x^2))

\int (e^{x} + \frac{14}{x} - \frac{3}{x ^{2}}) d x

e^{x} + 14 ln ∣ x ∣ + \frac{3}{x} + C

Solution steps

\int e^{x} + \frac{14}{x} - \frac{3}{x ^{2}} 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^{x} d x + \int \frac{14}{x} d x - \int \frac{3}{x ^{2}} d x

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

\int \frac{14}{x} d x = 14 ln ∣ x ∣

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

= e^{x} + 14 ln ∣ x ∣ - (- \frac{3}{x})

Simplify

= e^{x} + 14 ln ∣ x ∣ + \frac{3}{x}

Add a constant to the solution

= e^{x} + 14 ln ∣ x ∣ + \frac{3}{x} + C

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What is the integral of (e^x+(14)/x-3/(x^2)) ?
The integral of (e^x+(14)/x-3/(x^2)) is e^x+14ln|x|+3/x+C