What is the integral of sec(x)tan(x)+3/x-e^x ?

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

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integral of sec(x)tan(x)+3/x-e^x

\int sec (x) tan (x) + \frac{3}{x} - e^{x} d x

sec (x) + 3 ln ∣ x ∣ - e^{x} + C

Solution steps

\int sec (x) tan (x) + \frac{3}{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 sec (x) tan (x) d x + \int \frac{3}{x} d x - \int e^{x} d x

\int sec (x) tan (x) d x = sec (x)

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= sec (x) + 3 ln ∣ x ∣ - e^{x}

Add a constant to the solution

= sec (x) + 3 ln ∣ x ∣ - e^{x} + C

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