What is the integral of (e^x+3/x+sin(x)) ?

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

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integral of (e^x+3/x+sin(x))

\int (e^{x} + \frac{3}{x} + sin (x)) d x

e^{x} + 3 ln ∣ x ∣ - cos (x) + C

Solution steps

\int e^{x} + \frac{3}{x} + sin (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 e^{x} d x + \int \frac{3}{x} d x + \int sin (x) d x

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int sin (x) d x = - cos (x)

= e^{x} + 3 ln ∣ x ∣ - cos (x)

Add a constant to the solution

= e^{x} + 3 ln ∣ x ∣ - cos (x) + C

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