What is the integral of (5/x-3e^x) ?

The integral of (5/x-3e^x) is 5ln|x|-3e^x+C

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integral of (5/x-3e^x)

\int (\frac{5}{x} - 3 e^{x}) d x

5 ln ∣ x ∣ - 3 e^{x} + C

Solution steps

\int \frac{5}{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{5}{x} d x - \int 3 e^{x} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

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

= 5 ln ∣ x ∣ - 3 e^{x}

Add a constant to the solution

= 5 ln ∣ x ∣ - 3 e^{x} + C

(1 + x^{2})^{\frac{3}{2}}

\frac{d}{d x} (\frac{6 x}{( x ^{2} - 1 ) ^{2}})

\frac{\partial}{\partial x} ((3 x y - 2)^{2})

\int_{4}^{9} x d x

f (x) = sin (x) + x cos (x)

What is the integral of (5/x-3e^x) ?
The integral of (5/x-3e^x) is 5ln|x|-3e^x+C