What is the integral of (tan(x)-2) ?

The integral of (tan(x)-2) is -ln|cos(x)|-2x+C

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integral of (tan(x)-2)

\int (tan (x) - 2) d x

- ln ∣ cos (x) ∣ - 2 x + C

Solution steps

\int tan (x) - 2 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 tan (x) d x - \int 2 d x

\int tan (x) d x = - ln ∣ cos (x) ∣

\int 2 d x = 2 x

= - ln ∣ cos (x) ∣ - 2 x

Add a constant to the solution

= - ln ∣ cos (x) ∣ - 2 x + C

What is the integral of (tan(x)-2) ?
The integral of (tan(x)-2) is -ln|cos(x)|-2x+C