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

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

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integral of (sec(x)-tan(x))^2

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

- x + 2 tan (x) - 2 sec (x) + C

Solution steps

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

Expand

(sec (x) - tan (x))^{2} : sec^{2} (x) - 2 sec (x) tan (x) + tan^{2} (x)

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

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

\int 2 sec (x) tan (x) d x = 2 sec (x)

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

= tan (x) - 2 sec (x) - x + tan (x)

Simplify

= - x + 2 tan (x) - 2 sec (x)

Add a constant to the solution

= - x + 2 tan (x) - 2 sec (x) + C

\frac{d ^{2}}{d x ^{2}} (4 x^{5} - \frac{3}{x ^{2}})

\frac{\partial}{\partial x} (5 \frac{y}{x})

x \to 0 - lim (\frac{x}{3 x ^{4} - 15 x})

f (x) = (1 - x) (x^{2} - 3) 2, (2, - 1)

\int_{0}^{π} π (3 sin^{2} (x))^{2} d x

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