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Popular Calculus >

integral of tan(x)-1

Solution

\int tan (x) - 1 d x

Solution

- 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

Graph

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Frequently Asked Questions (FAQ)

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