What is the integral of (sec(2y)-csc(2y)) ?

The integral of (sec(2y)-csc(2y)) is 1/2 ln|tan(2y)+sec(2y)|-1/2 ln|tan(y)|+C

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integral of (sec(2y)-csc(2y))

\int (sec (2 y) - csc (2 y)) d y

\frac{1}{2} ln ∣ tan (2 y) + sec (2 y) ∣ - \frac{1}{2} ln ∣ tan (y) ∣ + C

Solution steps

\int sec (2 y) - csc (2 y) d y

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 (2 y) d y - \int csc (2 y) d y

\int sec (2 y) d y = \frac{1}{2} ln ∣ tan (2 y) + sec (2 y) ∣

\int csc (2 y) d y = \frac{1}{2} ln ∣ tan (y) ∣

= \frac{1}{2} ln ∣ tan (2 y) + sec (2 y) ∣ - \frac{1}{2} ln ∣ tan (y) ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ tan (2 y) + sec (2 y) ∣ - \frac{1}{2} ln ∣ tan (y) ∣ + C

x \to - 1 lim (1)

\int (x - 6)^{3} d x

\int_{- 3}^{2} - x^{2} - 2 x d x

\frac{d}{d x} (ln (x y + x - y - 1))

\frac{a - x}{a + x}

What is the integral of (sec(2y)-csc(2y)) ?
The integral of (sec(2y)-csc(2y)) is 1/2 ln|tan(2y)+sec(2y)|-1/2 ln|tan(y)|+C