What is the integral of (2e^x+6/x+5) ?

The integral of (2e^x+6/x+5) is 2e^x+6ln|x|+5x+C

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integral of (2e^x+6/x+5)

\int (2 e^{x} + \frac{6}{x} + 5) d x

2 e^{x} + 6 ln ∣ x ∣ + 5 x + C

Solution steps

\int 2 e^{x} + \frac{6}{x} + 5 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 2 e^{x} d x + \int \frac{6}{x} d x + \int 5 d x

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

\int \frac{6}{x} d x = 6 ln ∣ x ∣

\int 5 d x = 5 x

= 2 e^{x} + 6 ln ∣ x ∣ + 5 x

Add a constant to the solution

= 2 e^{x} + 6 ln ∣ x ∣ + 5 x + C

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What is the integral of (2e^x+6/x+5) ?
The integral of (2e^x+6/x+5) is 2e^x+6ln|x|+5x+C