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

Popular >

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{\partial}{\partial y} (2 x + y cos (x y))

\int_{0}^{2} 17 d x

e^{\frac{z}{z - 3}}

\frac{d ^{2} y}{d x ^{2}} = 2 x - 3

x \to 2 - lim (\frac{x + 2}{x ^{2} - 4})

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