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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

Simplify

= 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