What is the integral of (4x+5)/(2x)+e^x ?

The integral of (4x+5)/(2x)+e^x is 1/2 (4x+5ln|x|)+e^x+C

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integral of (4x+5)/(2x)+e^x

\int \frac{4 x + 5}{2 x} + e^{x} d x

\frac{1}{2} (4 x + 5 ln ∣ x ∣) + e^{x} + C

Solution steps

\int \frac{4 x + 5}{2 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{4 x + 5}{2 x} d x + \int e^{x} d x

\int \frac{4 x + 5}{2 x} d x = \frac{1}{2} (4 x + 5 ln ∣ x ∣)

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

= \frac{1}{2} (4 x + 5 ln ∣ x ∣) + e^{x}

Add a constant to the solution

= \frac{1}{2} (4 x + 5 ln ∣ x ∣) + e^{x} + C

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What is the integral of (4x+5)/(2x)+e^x ?
The integral of (4x+5)/(2x)+e^x is 1/2 (4x+5ln|x|)+e^x+C