What is the integral of sqrt(sec(x))tan(x) ?

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

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integral of sqrt(sec(x))tan(x)

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

2 sec (x) + C

Solution steps

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

Apply u-substitution

= \int \frac{1}{u} d u

Apply the Power Rule

= 2 u^{\frac{1}{2}}

Substitute back

u = sec (x)

= 2 sec^{\frac{1}{2}} (x)

Apply radical rule:

= 2 sec (x)

Add a constant to the solution

= 2 sec (x) + C

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