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

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

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

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

tan (x) + csc (x) + C

Solution steps

\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 - 3 lim (f (x) x)

y^{^{'}} = 8 y^{2} cos (t) + 7 y^{2} sin (4 t)

t an g e n t x^{3} - 2 x + 2

t an g e n t - 6 x^{2} + 5 x

d er i v a t i v e y = (ln (x))^{3}

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