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

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

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

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

2 sec (x) + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

= 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

\frac{d y}{d t} = e^{- t}

\frac{\partial}{\partial y} (2 x z)

e^{- 4}

y = x + 3, (1, 2)

sin (x) + \frac{7}{5} cot (x)

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