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

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

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integral of ((sec(x))^2-csc(x)cot(x))

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

tan (x) + csc (x) + C

Solution steps

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

Simplify

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

\int sec^{2} (x) d x = tan (x)

\int csc (x) cot (x) d x = - csc (x)

= tan (x) - (- csc (x))

Simplify

= tan (x) + csc (x)

Add a constant to the solution

= tan (x) + csc (x) + C

x \to 0 lim (\frac{x}{x})

\int sin (x) \cdot sin (3 x) d x

\int 2 cos^{2} (2 x) d x

\frac{d}{d x} (\frac{π x}{12})

x \to 0 lim ((1 + 2 x)^{\frac{1}{x}})

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