What is the integral of (5/x+e^x) ?

The integral of (5/x+e^x) is 5ln|x|+e^x+C

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integral of (5/x+e^x)

\int (\frac{5}{x} + e^{x}) d x

5 ln ∣ x ∣ + e^{x} + C

Solution steps

\int \frac{5}{x} + 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{5}{x} d x + \int e^{x} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

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

= 5 ln ∣ x ∣ + e^{x}

Add a constant to the solution

= 5 ln ∣ x ∣ + e^{x} + C

x \to - 1.001 lim (x^{3} - 1)

\frac{d}{d x} (3 x^{3} - 6 x)

\frac{d}{d x} (cos (x - a))

\int_{0}^{\frac{1}{5}} x arcsin (5 x) d x

\int e^{2 x^{2}} d x