What is the integral of (sec(x)+tan(x))/(cos(x)) ?

The integral of (sec(x)+tan(x))/(cos(x)) is tan(x)+sec(x)+C

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integral of (sec(x)+tan(x))/(cos(x))

\int \frac{sec ( x ) + tan ( x )}{cos ( x )} d x

tan (x) + sec (x) + C

Solution steps

\int \frac{sec ( x ) + tan ( x )}{cos ( x )} d x

Expand

\frac{sec ( x ) + tan ( x )}{cos ( x )} : \frac{sec ( x )}{cos ( x )} + \frac{tan ( x )}{cos ( x )}

= \int \frac{sec ( x )}{cos ( x )} + \frac{tan ( x )}{cos ( 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 \frac{sec ( x )}{cos ( x )} d x + \int \frac{tan ( x )}{cos ( x )} d x

\int \frac{sec ( x )}{cos ( x )} d x = tan (x)

\int \frac{tan ( x )}{cos ( x )} d x = sec (x)

= tan (x) + sec (x)

Add a constant to the solution

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

What is the integral of (sec(x)+tan(x))/(cos(x)) ?
The integral of (sec(x)+tan(x))/(cos(x)) is tan(x)+sec(x)+C