What is the integral of (tan(x)+1) ?

The integral of (tan(x)+1) is -ln|cos(x)|+x+C

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integral of (tan(x)+1)

\int (tan (x) + 1) d x

- ln ∣ cos (x) ∣ + x + C

Solution steps

\int tan (x) + 1 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 1 d x

\int tan (x) d x = - ln ∣ cos (x) ∣

\int 1 d x = x

= - ln ∣ cos (x) ∣ + x

Add a constant to the solution

= - ln ∣ cos (x) ∣ + x + C

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What is the integral of (tan(x)+1) ?
The integral of (tan(x)+1) is -ln|cos(x)|+x+C