What is the integral of (sec(x)+csc^2(x)) ?

The integral of (sec(x)+csc^2(x)) is ln|tan(x)+sec(x)|-cot(x)+C

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integral of (sec(x)+csc^2(x))

\int (sec (x) + csc^{2} (x)) d x

ln ∣ tan (x) + sec (x) ∣ - cot (x) + C

Solution steps

\int sec (x) + csc^{2} (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) d x + \int csc^{2} (x) d x

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

\int csc^{2} (x) d x = - cot (x)

= ln ∣ tan (x) + sec (x) ∣ - cot (x)

Add a constant to the solution

= ln ∣ tan (x) + sec (x) ∣ - cot (x) + C

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What is the integral of (sec(x)+csc^2(x)) ?
The integral of (sec(x)+csc^2(x)) is ln|tan(x)+sec(x)|-cot(x)+C