What is the integral of (5e^x-2/x) ?

The integral of (5e^x-2/x) is 5e^x-2ln|x|+C

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integral of (5e^x-2/x)

\int (5 e^{x} - \frac{2}{x}) d x

5 e^{x} - 2 ln ∣ x ∣ + C

Solution steps

\int 5 e^{x} - \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 5 e^{x} d x - \int \frac{2}{x} d x

\int 5 e^{x} d x = 5 e^{x}

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= 5 e^{x} - 2 ln ∣ x ∣

Add a constant to the solution

= 5 e^{x} - 2 ln ∣ x ∣ + C

y = x^{2}, y = 5 x

\frac{d}{d x} (ln (2 x - 3))

\frac{( 5 e ^{- s} )}{s + 1}

f (x) = 3 x + 7, at a = 6

\frac{d}{d y} (\frac{x}{( x + y ) ^{2}})

What is the integral of (5e^x-2/x) ?
The integral of (5e^x-2/x) is 5e^x-2ln|x|+C